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C₂×D₃×#3025 #72248135

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁵

Aliases

C₂×D₃×#3025

Splittings

Fitting	C₂×C₃×#3025 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#3025

Subgroups

	subgroup	G/H
center	C₂×C₄	D₃×#120
commutator, cosocle	C₂³×C₃	C₂⁶
Frattini	C₂³	C₂⁵×D₃
Fitting	C₂×C₃×#3025	C₂
socle	C₂²×C₃	C₂²×#120
hypercenter	C₂×#3025	D₃
hypocenter	C₃	C₂²×#3025
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#3025

46556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#23882, D₃×#498885, C₂×D₃×#87519, …
maximal normal subgroup of	C₂×D₃×#23882, D₃×#498885, D₃×#449496, …
maximal quotient of	D₃×#6437616, D₃×#6512843, D₃×#6454041
automorphism group of	C₂×#812

GAP

Past the SmallGroups library coverage — no SmallGroups id.