Finite Group Databasebeta

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C₂×#10707075 #72246019

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×#10707075

Splittings

Fitting	C₂×C₃×#2171 ⋊ C₂
Sylow	C₃ ⋊ C₂×#12068

Subgroups

	subgroup	G/H
center	C₂×C₄	#5014
commutator	C₃×C₈	C₂³×C₈
Frattini	C₄×C₈	C₂³×D₃
Fitting	C₂×C₃×#2171	C₂
socle	C₂²×C₃	#1580
prime radical	C₂×#5194	C₄
cosocle	C₃×C₄×C₈	C₂⁴
hypercenter	C₂×#2171	D₃
hypocenter	C₃	C₂×#12068
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#346 ◁ C₂×#2171

940 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#12068
maximal normal subgroup of	C₂×D₃×#12068

GAP

Past the SmallGroups library coverage — no SmallGroups id.