Finite Group Databasebeta

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C₂×#13091420 #72244104

order	2916
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃³ · Schur multiplier (H₂) = C₂×C₃³

Aliases

C₂×#13091420

Splittings

Fitting	C₂×#10624869 ⋊ C₂
Sylow	#10624869 ⋊ C₂²

Subgroups

	subgroup	G/H
center	C₂×C₉	C₃×(C₃⋊D₃)⋊C₃
commutator, cosocle	C₃³	C₂²×C₃³
Frattini	C₃²	C₂×C₃³×D₃
Fitting	C₂×#10624869	C₂
socle	C₂×C₃²	C₃³×D₃
prime radical	C₂×(C₃⋊D₃)⋊H(3,𝔽₃)	C₃
hypercenter	C₂×C₃×C₉	(C₃⋊D₃)⋊C₃
hypocenter	C₃²	C₂²×#737
LCS	G ▷ C₃³ ▷ C₃²
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₃×C₉

1019 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 108

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#72221845, C₂×#72221863
maximal normal subgroup of	C₂×#72221863
maximal quotient of	C₂×#72221846

GAP

Past the SmallGroups library coverage — no SmallGroups id.