Finite Group Databasebeta

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C₂×#11772193 #72255495

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²×C₃

Aliases

C₂×#11772193

Splittings

C₃² ⋊ C₂×#1369

Subgroups

	subgroup	G/H
center	C₂×C₄	#63644
commutator	C₃²×C₈	C₂²×C₈
Frattini	C₄×C₈	C₂²×C₃⋊D₃
Fitting	C₂×C₃²×#346	C₂
socle	C₂²×C₃²	#334
prime radical	C₂³×C₃²	#108
cosocle	C₃²×C₄×C₈	C₂³
hypercenter	C₂×#346	C₃⋊D₃
hypocenter	C₃²	C₂×#1369
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#346

666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 576

Conjugacy classes & character table

384 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃⋊D₃×#1369
maximal normal subgroup of	C₂×C₃⋊D₃×#1369

GAP

Past the SmallGroups library coverage — no SmallGroups id.