C₂×D₈₀₉₁ #44569048

order	32364
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₆₁₈₂
direct product	C₂×D₈₀₉₁
unambiguous semidirect product	(C₂×C₉)⋊D₈₉₉
unambiguous semidirect product	(C₂×C₂₉)⋊D₂₇₉
unambiguous semidirect product	(C₂×C₃₁)⋊D₂₆₁

Splittings

Fitting	C₂×C₉×C₂₉×C₃₁ ⋊ C₂
derived, Hall	C₉×C₂₉×C₃₁ ⋊ C₂²
Hall	C₂₉×C₃₁ ⋊ C₂×D₉
Hall	C₉×C₃₁ ⋊ C₂×D₂₉
Hall	C₉×C₂₉ ⋊ C₂×D₃₁
Sylow	C₃₁ ⋊ C₂×D₂₆₁
Sylow	C₂₉ ⋊ C₂×D₂₇₉
Sylow	C₉ ⋊ C₂×D₈₉₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₈₀₉₁
commutator, cosocle, hypocenter	C₉×C₂₉×C₃₁	C₂²
Frattini	C₃	C₂×D₂₆₉₇
Fitting	C₂×C₉×C₂₉×C₃₁	C₂
socle	C₂×C₃×C₂₉×C₃₁	D₃
LCS	G ▷ C₉×C₂₉×C₃₁
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 16182

A minimal faithful permutation representation — 2 generators on 71 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);(4,11)(5,10)(6,9)(7,8)(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)(42,71)(43,70)(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(56,57)

Conjugacy classes & character table

8094 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃₂₃₆₄
maximal normal subgroup of	D₃₂₃₆₄
maximal quotient of	Dic₁₆₁₈₂, D₃₂₃₆₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 34);

C2×D8091 #44569048