C₂×D₂₈₉₁ #26040586

order	11564
automorphism	Aut(G) order 14084952
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₅₇₈₂
direct product	C₂×D₂₈₉₁
unambiguous semidirect product	(C₂×C₄₉)⋊D₅₉
unambiguous semidirect product	(C₂×C₅₉)⋊D₄₉

Splittings

Fitting	C₂×C₄₉×C₅₉ ⋊ C₂
derived, Hall	C₄₉×C₅₉ ⋊ C₂²
Sylow	C₅₉ ⋊ C₂×D₄₉
Sylow	C₄₉ ⋊ C₂×D₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₂₈₉₁
commutator, cosocle, hypocenter	C₄₉×C₅₉	C₂²
Frattini	C₇	C₂×D₄₁₃
Fitting	C₂×C₄₉×C₅₉	C₂
socle	C₂×C₇×C₅₉	D₇
LCS	G ▷ C₄₉×C₅₉
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 110
transitive degree	μ_t(G) = 5782

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);(4,51)(5,50)(6,49)(7,48)(8,47)(9,46)(10,45)(11,44)(12,43)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)(53,110)(54,109)(55,108)(56,107)(57,106)(58,105)(59,104)(60,103)(61,102)(62,101)(63,100)(64,99)(65,98)(66,97)(67,96)(68,95)(69,94)(70,93)(71,92)(72,91)(73,90)(74,89)(75,88)(76,87)(77,86)(78,85)(79,84)(80,83)(81,82)

Conjugacy classes & character table

2894 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅₉⋊(D₄₉⋊C₃), D₃×D₂₈₉₁, C₂×C₃×D₂₈₉₁, …
maximal normal subgroup of	C₂×C₅₉⋊(D₄₉⋊C₃), C₂×C₃×D₂₈₉₁, D₁₁₅₆₄
maximal quotient of	D₃×D₂₈₉₁, C₂×C₃×D₂₈₉₁, C₂×D₈₆₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11564, 9);

C2×D2891 #26040586