C₂×D₇₉₄₃ #44540949

order	31772
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₅₈₈₆
direct product	C₂×D₇₉₄₃
unambiguous semidirect product	(C₂×C₄₇)⋊D₁₆₉
unambiguous semidirect product	(C₂×C₁₆₉)⋊D₄₇

Splittings

Fitting	C₂×C₄₇×C₁₆₉ ⋊ C₂
derived, Hall	C₄₇×C₁₆₉ ⋊ C₂²
Sylow	C₁₆₉ ⋊ C₂×D₄₇
Sylow	C₄₇ ⋊ C₂×D₁₆₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₇₉₄₃
commutator, cosocle, hypocenter	C₄₇×C₁₆₉	C₂²
Frattini	C₁₃	C₂×D₆₁₁
Fitting	C₂×C₄₇×C₁₆₉	C₂
socle	C₂×C₁₃×C₄₇	D₁₃
LCS	G ▷ C₄₇×C₁₆₉
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 218
transitive degree	μ_t(G) = 15886

A minimal faithful permutation representation — 2 generators on 218 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171)(172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218);(4,171)(5,170)(6,169)(7,168)(8,167)(9,166)(10,165)(11,164)(12,163)(13,162)(14,161)(15,160)(16,159)(17,158)(18,157)(19,156)(20,155)(21,154)(22,153)(23,152)(24,151)(25,150)(26,149)(27,148)(28,147)(29,146)(30,145)(31,144)(32,143)(33,142)(34,141)(35,140)(36,139)(37,138)(38,137)(39,136)(40,135)(41,134)(42,133)(43,132)(44,131)(45,130)(46,129)(47,128)(48,127)(49,126)(50,125)(51,124)(52,123)(53,122)(54,121)(55,120)(56,119)(57,118)(58,117)(59,116)(60,115)(61,114)(62,113)(63,112)(64,111)(65,110)(66,109)(67,108)(68,107)(69,106)(70,105)(71,104)(72,103)(73,102)(74,101)(75,100)(76,99)(77,98)(78,97)(79,96)(80,95)(81,94)(82,93)(83,92)(84,91)(85,90)(86,89)(87,88)(173,218)(174,217)(175,216)(176,215)(177,214)(178,213)(179,212)(180,211)(181,210)(182,209)(183,208)(184,207)(185,206)(186,205)(187,204)(188,203)(189,202)(190,201)(191,200)(192,199)(193,198)(194,197)(195,196)

Conjugacy classes & character table

7946 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃₁₇₇₂
maximal normal subgroup of	D₃₁₇₇₂
maximal quotient of	Dic₁₅₈₈₆, D₃₁₇₇₂

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31772, 9);

C2×D7943 #44540949