Finite Group Databasebeta

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C3×#67706 #11770856

order1152
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×#67706

Splittings

SylowC32 ⋊ #1283

Subgroups

subgroupG/H
centerC2×C3×C4#217
commutatorC22×C3C3×C4×C8
FrattiniC2×C42C2×C3×D3
FittingC2×C32×C4⋊C8C2
socleC22×C32#95
prime radicalC23×C32C42
cosocleC2×C3×C42C22×C3
hypercenterC2×C3×C4⋊C8D3
hypocenterC3C3×#1283
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

389 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4867);