Finite Group Databasebeta

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C₃⋊D₃×#1312 #72245394

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₆ · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

C₃⋊D₃×#1312

Splittings

Fitting	C₃²×#1312 ⋊ C₂
Sylow	C₃² ⋊ C₂×#1312

Subgroups

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₂×C₄×C₁₆
Fitting	C₃²×#1312	C₂
socle	C₂²×C₃²	C₂×C₄×C₈
prime radical	C₂²×C₃⋊D₃	C₄×C₈
cosocle	C₃²×C₄×C₈	C₂³
hypercenter	#1312	C₃⋊D₃
hypocenter	C₃²	C₂×#1312
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄×C₈ ◁ #1312

1050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1152

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃⋊D₃×#7053
maximal normal subgroup of	C₃⋊D₃×#7053
maximal quotient of	C₃⋊D₃×#7053, C₃⋊D₃×#7332

GAP

Past the SmallGroups library coverage — no SmallGroups id.