Finite Group Databasebeta

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C₂×#6293 #89036

order	432
isoclinism	isoclinic class of #6290
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²×C₃

Aliases

Splittings

C₃³ ⋊ C₂×Q₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	D₃×C₃⋊D₃
commutator, cosocle	C₂×C₃³	C₂³
Frattini	C₂	C₂×D₃×C₃⋊D₃
Fitting, socle, prime radical	C₂²×C₃³	C₂²
hypocenter	C₃³	C₂×Q₈
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂²

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 19 points:

(1,2)(4,5)(7,8)(9,10,11)(12,14,15,19)(13,16,17,18);(3,4,5)(10,11)(12,13,15,17)(14,18,19,16);(1,2)(6,7,8)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11722730, #11722942, #11722943, …
maximal normal subgroup of	#11722730, #11722942, #11722943, …
maximal quotient of	#11723447, #11723450, #11723454, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 683);