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C₂×#3673 #63494

order	288
isoclinism	isoclinic class of #3672
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

Splittings

Fitting	C₂×D₄×C₉ ⋊ C₂
Sylow	C₉ ⋊ C₂×D₈

Subgroups

	subgroup	G/H
center	C₂²	#611
commutator, cosocle	C₄×C₉	C₂³
Frattini	C₃×C₄	C₂²×D₃
Fitting	C₂×D₄×C₉	C₂
socle	C₂²×C₃	#67
hypercenter	C₂×D₄	D₉
hypocenter	C₉	C₂×D₈
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

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:

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10588429, #10588436, #10588453, …
maximal normal subgroup of	#10588429, #10588436, #10588453, …
maximal quotient of	C₂×#63366, C₂×#63369, #10588650, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 142);