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C₄×C₃⋊#157 #88990

order	432
isoclinism	isoclinic class of C₃⋊#157
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₃×C₄

Aliases

C₄×C₃⋊#157

Splittings

Fitting	C₃³×C₄ ⋊ C₄
derived, Sylow	C₃³ ⋊ C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₄	C₃⋊#157
commutator, hypocenter	C₃³	C₄²
Frattini	C₂	C₂×C₃⋊#157
Fitting	C₃³×C₄	C₄
socle	C₂×C₃³	C₂×C₄
prime radical, cosocle	C₂×C₃×C₃⋊D₃	C₂²
LCS	G ▷ C₃³
UCS	C₁ ◁ C₄

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 13 points:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11722703, #11722705, #11722710, …
maximal normal subgroup of	#11722703, #11722705, #11722710, …
maximal quotient of	C₈×C₃⋊#157, #11723092, C₄×C₃⋊#622, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 637);