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C₂×C₈×D₉ #63462

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

Aliases

C₂×C₈×D₉

Splittings

Fitting	C₂×C₈×C₉ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂²×C₈

Subgroups

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

114 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)(12,14)(13,17)(15,18)(16,19);(3,4,5,7,6,8,9,10)(11,16,14,13,18,15,17,12,19);(1,2)

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₂×D₉)⋊C₁₆, C₄×C₈×D₉, C₈×D₃₆, …
maximal normal subgroup of	(C₂×D₉)⋊C₁₆, C₄×C₈×D₉, C₈×D₃₆, …
maximal quotient of	C₈×Dic₁₈, C₄×C₈×D₉, #10588367, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 110);