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C₂×#6053 #87914

order	400
isoclinism	isoclinic class of #6053
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

Splittings

Fitting, socle	C₂×C₅² ⋊ C₈
derived, Sylow	C₅² ⋊ C₂×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂	#6053
commutator, hypocenter	C₅²	C₂×C₈
Frattini	C₁	G
Fitting, socle	C₂×C₅²	C₈
prime radical	C₂×C₅⋊D₅	C₄
cosocle	#1043	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 20

A minimal faithful permutation representation — 2 generators on 12 points:

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

Conjugacy classes & character table

22 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#6053⋊C₄, #11717304, #11717305, …
maximal normal subgroup of	#6053⋊C₄, #11717304, #11717305, …
maximal quotient of	#11717315, #11717316, C₄×#6053, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 208);