Finite Group Databasebeta

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C₂×C₃⋊D₃×#1369 #72269679

order	4608
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

C₂×C₃⋊D₃×#1369

Splittings

Fitting	C₂×C₃²×#1369 ⋊ C₂
Sylow	C₃² ⋊ C₂²×#1369

Subgroups

	subgroup	G/H
center	C₂×C₄	C₃⋊D₃×#106
commutator	C₃²×C₈	C₂³×C₈
Frattini	C₄×C₈	C₂³×C₃⋊D₃
Fitting	C₂×C₃²×#1369	C₂
socle	C₂²×C₃²	C₂×#334
prime radical	C₂³×C₃⋊D₃	#108
cosocle	C₃²×C₄×C₈	C₂⁴
hypercenter	C₂×#1369	C₃⋊D₃
hypocenter	C₃²	C₂²×#1369
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#1369

3132 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.

GAP

Past the SmallGroups library coverage — no SmallGroups id.