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C₄×#1113 #89043

order	432
isoclinism	isoclinic class of #1113
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

Splittings

Fitting	C₃³×C₄ ⋊ C₂²
derived, Sylow	C₃³ ⋊ C₂²×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₄	#1113
commutator, hypocenter	C₃³	C₂²×C₄
Frattini	C₂	C₂×#1113
Fitting	C₃³×C₄	C₂²
socle, cosocle	C₂×C₃³	C₂³
prime radical	C₂×#1113	C₂
LCS	G ▷ C₃³
UCS	C₁ ◁ C₄

270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 13 points:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11722751, #11722780, #11722814, …
maximal normal subgroup of	#11722751, #11722780, #11722814, …
maximal quotient of	C₈×#1113, #11723645, #11723651, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 690);