C₂×D₄₁₈₃ #30660219

order	16732
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₈₃₆₆
direct product	C₂×D₄₁₈₃
unambiguous semidirect product	(C₂×C₄₇)⋊D₈₉
unambiguous semidirect product	(C₂×C₈₉)⋊D₄₇

Splittings

Fitting, socle	C₂×C₄₇×C₈₉ ⋊ C₂
derived, Hall	C₄₇×C₈₉ ⋊ C₂²
Sylow	C₈₉ ⋊ C₂×D₄₇
Sylow	C₄₇ ⋊ C₂×D₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₄₁₈₃
commutator, cosocle, hypocenter	C₄₇×C₈₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₄₇×C₈₉	C₂
LCS	G ▷ C₄₇×C₈₉
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 138
transitive degree	μ_t(G) = 8366

A minimal faithful permutation representation — 2 generators on 138 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);(4,49)(5,48)(6,47)(7,46)(8,45)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(51,138)(52,137)(53,136)(54,135)(55,134)(56,133)(57,132)(58,131)(59,130)(60,129)(61,128)(62,127)(63,126)(64,125)(65,124)(66,123)(67,122)(68,121)(69,120)(70,119)(71,118)(72,117)(73,116)(74,115)(75,114)(76,113)(77,112)(78,111)(79,110)(80,109)(81,108)(82,107)(83,106)(84,105)(85,104)(86,103)(87,102)(88,101)(89,100)(90,99)(91,98)(92,97)(93,96)(94,95)

Conjugacy classes & character table

4186 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₆₇₃₂, C₂×D₁₂₅₄₉
maximal normal subgroup of	D₁₆₇₃₂
maximal quotient of	Dic₈₃₆₆, D₁₆₇₃₂, C₂×D₁₂₅₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16732, 9);

C2×D4183 #30660219