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C₂²×#622 #64291

order	288
isoclinism	isoclinic class of #157
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂²×#622

Splittings

C₃² ⋊ C₂²×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂³	#157
commutator, hypocenter	C₃²	C₂²×C₈
Frattini	C₂	C₂²×#157
Fitting, socle, prime radical	C₂³×C₃²	C₄
cosocle	C₃⋊Dic₃	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂³

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 18 points:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10590075, #10590097, #10590207, …
maximal normal subgroup of	#10590075, #10590097, #10590207, …
maximal quotient of	C₂²×#3708, C₂×#63773, C₂×C₄×#622, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 939);