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C₂²×#1043 #87922

order	400
isoclinism	isoclinic class of #1043
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

Splittings

Fitting, socle	C₂²×C₅² ⋊ C₄
derived, Sylow	C₅² ⋊ C₂²×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	#1043
commutator, hypocenter	C₅²	C₂²×C₄
Frattini	C₁	G
Fitting, socle	C₂²×C₅²	C₄
prime radical	C₂²×C₅⋊D₅	C₂
cosocle	C₅⋊D₅	C₂³
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 100

A minimal faithful permutation representation — 3 generators on 14 points:

(6,7,8,9)(11,12,13,14);(3,4)(5,6,7,9,8);(1,2)(10,11,12,14,13)

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716776, #11716874, C₂²⋊#6053, …
maximal normal subgroup of	#11716776, #11716874, C₂²⋊#6053, …
maximal quotient of	C₂×#87855, C₂×#87856, #11717435, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 216);