Finite Group Databasebeta

← Prev (#88241) Next (#88243) →

C₂²×#1057 #88242

order	416
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

Splittings

C₁₃ ⋊ C₂²×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂³	#261
commutator, hypocenter	C₁₃	C₂²×C₈
Frattini	C₂	C₂²×#261
Fitting, socle, prime radical	C₂³×C₁₃	C₄
cosocle	Dic₁₃	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂³

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 25 points:

(5,6,7,9,8,10,11,12)(14,15,16,18)(17,20,21,25)(19,23,24,22);(3,4)(13,14,17,20,24,18,22,23,15,19,25,21,16);(1,2)

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11718290, #11719062, #11719063, …
maximal normal subgroup of	#11718290, #11719062, #11719063, …
maximal quotient of	C₂²×#6092, C₂×#88106, C₂×C₄×#1057, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 209);