Finite Group Databasebeta

← Prev (#87880) Next (#87882) →

C₂×#6036 #87881

order	400
isoclinism	isoclinic class of D₅²
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

Splittings

C₅² ⋊ C₂²×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	D₅²
commutator, hypocenter	C₅²	C₂²×C₄
Frattini	C₂	C₂×D₅²
Fitting, socle	C₂²×C₅²	C₂²
prime radical	C₂²×C₅⋊D₅	C₂
cosocle	C₂×C₅²	C₂³
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11716754, #11716776, #11716795, …
maximal normal subgroup of	#11716754, #11716776, #11716795, …
maximal quotient of	C₂×#87767, #11716935, #11716936, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 175);