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C₂²×C₉⋊C₈ #63482

order	288
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×C₉⋊C₈

Splittings

C₉ ⋊ C₂²×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₄	D₉
commutator, hypocenter	C₉	C₂²×C₈
Frattini	C₃×C₄	C₂²×D₃
Fitting	C₂²×C₄×C₉	C₂
socle, prime radical	C₂³×C₃	Dic₃
cosocle	C₄×C₉	C₂³
LCS	G ▷ C₉
UCS	C₁ ◁ C₂²×C₄

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2)(3,4)(5,6,7,9,8,10,11,12)(14,16)(15,19)(17,18)(20,21);(3,4)(13,21,16,19,18,17,15,14,20);(1,2)

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10588200, #10588206, #10588228, …
maximal normal subgroup of	#10588200, #10588206, #10588228, …
maximal quotient of	C₂×C₄×C₉⋊C₈, C₂×C₄⋊(C₉⋊C₈), #10588605, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 130);