Finite Group Databasebeta

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C₂×#11864781 #72269124

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂×#11864781

Splittings

Fitting	C₂×C₃²×#100 ⋊ C₂²
Sylow	C₃² ⋊ C₂²×#453

Subgroups

	subgroup	G/H
center	C₂²	#10594258
commutator, cosocle	C₂×C₃²×C₄	C₂⁵
Frattini	C₂×C₄	C₂³×D₃²
Fitting	C₂×C₃²×#100	C₂²
socle	C₂²×C₃²	C₂×#120
hypercenter	C₂×#100	D₃²
hypocenter	C₃²	C₂²×#453
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#100

11836 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.