Finite Group Databasebeta

← Prev (#72253404) Next (#72253406) →

C₂×D₃×#2679 #72253405

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

C₂×D₃×#2679

Splittings

Fitting	C₂×C₃×#2679 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#2679

Subgroups

	subgroup	G/H
center	C₂⁴	C₂⁴×D₃
commutator, cosocle	C₂³×C₃	C₂⁶
Frattini	C₂³	C₂⁵×D₃
Fitting	C₂×C₃×#2679	C₂
socle	C₂⁴×C₃	C₂⁵
hypercenter	C₂×#2679	D₃
hypocenter	C₃	C₂²×#2679
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#2679

59684 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#7695992, D₃×#7659307, D₃×#147779
maximal normal subgroup of	D₃×#7695992, D₃×#7659307, D₃×#147779
maximal quotient of	C₂×D₃×#15947

GAP

Past the SmallGroups library coverage — no SmallGroups id.