Finite Group Databasebeta

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C3×#71773 #11776288

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#71773

Splittings

SylowC32 ⋊ #1546

Subgroups

subgroupG/H
centerC22×C3C2×#217
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC2×C32×C4⋊Q8C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC3×C42C23×C3
hypercenterC2×C3×C4⋊Q8D3
hypocenterC3C3×#1546
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊Q8

625 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 10299);