C₂×D₄₁₈₇ #30660451

order	16748
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₈₃₇₄
direct product	C₂×D₄₁₈₇
unambiguous semidirect product	(C₂×C₅₃)⋊D₇₉
unambiguous semidirect product	(C₂×C₇₉)⋊D₅₃

Splittings

Fitting, socle	C₂×C₅₃×C₇₉ ⋊ C₂
derived, Hall	C₅₃×C₇₉ ⋊ C₂²
Sylow	C₇₉ ⋊ C₂×D₅₃
Sylow	C₅₃ ⋊ C₂×D₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₄₁₈₇
commutator, cosocle, hypocenter	C₅₃×C₇₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅₃×C₇₉	C₂
LCS	G ▷ C₅₃×C₇₉
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 134
transitive degree	μ_t(G) = 8374

A minimal faithful permutation representation — 2 generators on 134 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);(4,55)(5,54)(6,53)(7,52)(8,51)(9,50)(10,49)(11,48)(12,47)(13,46)(14,45)(15,44)(16,43)(17,42)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(57,134)(58,133)(59,132)(60,131)(61,130)(62,129)(63,128)(64,127)(65,126)(66,125)(67,124)(68,123)(69,122)(70,121)(71,120)(72,119)(73,118)(74,117)(75,116)(76,115)(77,114)(78,113)(79,112)(80,111)(81,110)(82,109)(83,108)(84,107)(85,106)(86,105)(87,104)(88,103)(89,102)(90,101)(91,100)(92,99)(93,98)(94,97)(95,96)

Conjugacy classes & character table

4190 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₁₆₇₄₈, C₂×D₁₂₅₆₁
maximal normal subgroup of	D₁₆₇₄₈
maximal quotient of	Dic₈₃₇₄, D₁₆₇₄₈, C₂×D₁₂₅₆₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16748, 9);

C2×D4187 #30660451