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C2×C3×#5032 #11865246

order1152
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C27

Aliases

direct productC2×C3×#5032

Splittings

FittingC2×C32×#120 ⋊ C2
SylowC32 ⋊ C2×B(4,𝔽2)

Subgroups

subgroupG/H
centerC22×C3#937
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#120C2
socleC22×C32#120
hypercenterC2×C3×#120D3
hypocenterC3C2×C3×B(4,𝔽2)
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×#120

2367 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×#5032, C2×C3×#10593244, C2×#11865254, …
maximal normal subgroup ofC2×#11865254, C2×C3×D3×B(4,𝔽2), #72252270, …
maximal quotient ofC3×D3×#5032, C3×#10943957, C3×#10767815, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 99257);