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C₂×Dic₅₅ #89184

order	440
isoclinism	isoclinic class of D₅₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×Dic₅₅
unambiguous semidirect product	(C₂×C₁₁)⋊Dic₅

Splittings

derived, Hall	C₅×C₁₁ ⋊ C₂×C₄
Sylow	C₁₁ ⋊ C₂×Dic₅
Sylow	C₅ ⋊ C₂×Dic₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	D₅₅
commutator, hypocenter	C₅×C₁₁	C₂×C₄
Frattini	C₂	C₂×D₅₅
Fitting, socle, prime radical	C₂²×C₅×C₁₁	C₂
cosocle	C₂×C₅×C₁₁	C₂²
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂²

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 440

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2)(3,4,5,6)(8,9)(10,11)(13,14)(15,16)(17,18)(19,20)(21,22);(1,2)(7,8,10,11,9)(12,13,15,17,19,21,22,20,18,16,14)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₅×Dic₁₁, (C₂×D₁₁)⋊Dic₅, #11724885, …
maximal normal subgroup of	Dic₅×Dic₁₁, (C₂×D₁₁)⋊Dic₅, #11724885, …
maximal quotient of	C₂×C₁₁⋊#168, #11724928, C₄×Dic₅₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 37);