C₂×D₉₆₃ #16838704

order	3852
automorphism	Aut(G) order 1224936
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₉₂₆
direct product	C₂×D₉₆₃
unambiguous semidirect product	(C₂×C₉)⋊D₁₀₇
unambiguous semidirect product	(C₂×C₁₀₇)⋊D₉

Splittings

Fitting	C₂×C₉×C₁₀₇ ⋊ C₂
derived, Hall	C₉×C₁₀₇ ⋊ C₂²
Sylow	C₁₀₇ ⋊ C₂×D₉
Sylow	C₉ ⋊ C₂×D₁₀₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₆₃
commutator, cosocle, hypocenter	C₉×C₁₀₇	C₂²
Frattini	C₃	C₂×D₃₂₁
Fitting	C₂×C₉×C₁₀₇	C₂
socle	C₂×C₃×C₁₀₇	D₃
LCS	G ▷ C₉×C₁₀₇
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 118
transitive degree	μ_t(G) = 1926

A minimal faithful permutation representation — 2 generators on 118 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);(4,11)(5,10)(6,9)(7,8)(13,118)(14,117)(15,116)(16,115)(17,114)(18,113)(19,112)(20,111)(21,110)(22,109)(23,108)(24,107)(25,106)(26,105)(27,104)(28,103)(29,102)(30,101)(31,100)(32,99)(33,98)(34,97)(35,96)(36,95)(37,94)(38,93)(39,92)(40,91)(41,90)(42,89)(43,88)(44,87)(45,86)(46,85)(47,84)(48,83)(49,82)(50,81)(51,80)(52,79)(53,78)(54,77)(55,76)(56,75)(57,74)(58,73)(59,72)(60,71)(61,70)(62,69)(63,68)(64,67)(65,66)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₅×D₉₆₃, C₂×D₄₈₁₅, C₂×C₅×D₉₆₃, …
maximal normal subgroup of	C₂×C₅×D₉₆₃, C₂×C₇×D₉₆₃, D₃₈₅₂
maximal quotient of	D₅×D₉₆₃, C₂×D₄₈₁₅, C₂×C₅×D₉₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3852, 10);

C2×D963 #16838704