Finite Group Databasebeta

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C3×#67678 #11770833

order1152
automorphism?
homologyAbelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC3×#67678

Splittings

SylowC32 ⋊ #1282

Subgroups

subgroupG/H
centerC2×C3×C4(C2×D3)⋊C4
commutatorC22×C3C3×C4×C8
FrattiniC23×C4C2×C3×D3
FittingC2×C32×C22⋊C8C2
socleC22×C32#95
prime radicalC24×C32C2×C4
cosocleC23×C3×C4C22×C3
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C3×#1282
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

557 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

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, 4844);