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C₄×D₅₅ #89182

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

Aliases

C₄×D₅₅

Splittings

Fitting	C₄×C₅×C₁₁ ⋊ C₂
derived, Hall	C₅×C₁₁ ⋊ C₂×C₄
Sylow	C₁₁ ⋊ C₄×D₅
Sylow	C₅ ⋊ C₄×D₁₁

Subgroups

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

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 220

A minimal faithful permutation representation — 2 generators on 20 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11724867, #11724870, C₈×D₅₅, …
maximal normal subgroup of	#11724867, #11724870, C₈×D₅₅, …
maximal quotient of	C₈×D₅₅, #11724923, C₄×Dic₅₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 35);