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C₂×#6033 #87859

order	400
isoclinism	isoclinic class of #1043
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

Splittings

C₅² ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	#1043
commutator, hypocenter	C₅²	C₂×C₈
Frattini	C₂	C₂×#1043
Fitting, socle, prime radical	C₂²×C₅²	C₄
cosocle	#1039	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 400

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716777, #11716778, #11716779, …
maximal normal subgroup of	#11716777, #11716778, #11716779, …
maximal quotient of	C₂×#87764, #11716866, C₄×#6033, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 153);