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D₄×C₃⋊Dic₃ #64143

order	288
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³×C₃

Aliases

D₄×C₃⋊Dic₃

Splittings

C₃² ⋊ C₄×D₄

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₂²×C₄
Fitting, prime radical	C₂×C₃²×D₄	C₂
socle, cosocle	C₂²×C₃²	C₂³
hypercenter	C₂×D₄	C₃⋊D₃
hypocenter	C₃²	C₄×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×D₄

282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 14 points:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₄⋊#622, #10591435, #10591436, …
maximal normal subgroup of	D₄⋊#622, #10591435, #10591436, …
maximal quotient of	C₂²⋊C₄×C₃⋊Dic₃, #10592649, #10592650, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 791);