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C₂³×Dic₉ #63717

order	288
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂³×Dic₉

Splittings

C₉ ⋊ C₂³×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁴	D₉
commutator, hypocenter	C₉	C₂³×C₄
Frattini	C₂×C₃	C₂³×D₃
Fitting	C₂⁴×C₉	C₂
socle, prime radical	C₂⁴×C₃	D₃
cosocle	C₂×C₉	C₂⁴
LCS	G ▷ C₉
UCS	C₁ ◁ C₂⁴

354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 4 generators on 19 points:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂²⋊C₄×Dic₉, #10588622, #10588623, …
maximal normal subgroup of	C₂²⋊C₄×Dic₉, #10588622, #10588623, …
maximal quotient of	C₂³×C₉⋊C₈, C₂²×#3667, C₂²×C₄×Dic₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 365);