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C₂×#3664 #63465

order	288
isoclinism	isoclinic class of Dic₃₆
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Fitting	C₂×C₈×C₉ ⋊ C₂
Sylow	C₉ ⋊ C₂×SD₁₆

Subgroups

	subgroup	G/H
center	C₂²	D₃₆
commutator, cosocle	C₄×C₉	C₂³
Frattini	C₃×C₄	C₂²×D₃
Fitting	C₂×C₈×C₉	C₂
socle	C₂²×C₃	D₁₂
prime radical	C₂×D₃₆	C₂
hypercenter	C₂×C₈	D₉
hypocenter	C₉	C₂×SD₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

102 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:

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

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×#3664, #10588375, #10588378, …
maximal normal subgroup of	C₄×#3664, #10588375, #10588378, …
maximal quotient of	#10588360, #10588361, C₄×#3664, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 113);