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C₂×C₄×C₃⋊Dic₃ #64131

order	288
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

C₂×C₄×C₃⋊Dic₃

Splittings

C₃² ⋊ C₂×C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₄	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₄²
Frattini	C₂²	C₂²×C₃⋊D₃
Fitting	C₂²×C₃²×C₄	C₂
socle, prime radical	C₂³×C₃²	C₂²
cosocle	C₂²×C₃²	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂²×C₄

324 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 288

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

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10589156, #10589160, #10589398, …
maximal normal subgroup of	#10589156, #10589160, #10589398, …
maximal quotient of	C₂×C₄×C₃⋊(C₃⋊C₈), C₂×#63630, C₄×#3748, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 779);