C₂×D₂₈₆₇ #26039731

order	11468
automorphism	Aut(G) order 15825840
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₅₇₃₄
direct product	C₂×D₂₈₆₇
unambiguous semidirect product	(C₂×C₄₇)⋊D₆₁
unambiguous semidirect product	(C₂×C₆₁)⋊D₄₇

Splittings

Fitting, socle	C₂×C₄₇×C₆₁ ⋊ C₂
derived, Hall	C₄₇×C₆₁ ⋊ C₂²
Sylow	C₆₁ ⋊ C₂×D₄₇
Sylow	C₄₇ ⋊ C₂×D₆₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₂₈₆₇
commutator, cosocle, hypocenter	C₄₇×C₆₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₄₇×C₆₁	C₂
LCS	G ▷ C₄₇×C₆₁
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 110
transitive degree	μ_t(G) = 5734

A minimal faithful permutation representation — 2 generators on 110 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);(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)(51,110)(52,109)(53,108)(54,107)(55,106)(56,105)(57,104)(58,103)(59,102)(60,101)(61,100)(62,99)(63,98)(64,97)(65,96)(66,95)(67,94)(68,93)(69,92)(70,91)(71,90)(72,89)(73,88)(74,87)(75,86)(76,85)(77,84)(78,83)(79,82)(80,81)

Conjugacy classes & character table

2870 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄₇⋊(D₆₁⋊C₃), D₃×D₂₈₆₇, C₂×C₃×D₂₈₆₇, …
maximal normal subgroup of	C₂×C₄₇⋊(D₆₁⋊C₃), C₂×C₃×D₂₈₆₇, D₁₁₄₆₈
maximal quotient of	D₃×D₂₈₆₇, C₂×C₃×D₂₈₆₇, C₂×D₈₆₀₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11468, 9);

C2×D2867 #26039731