Finite Group Databasebeta

C3×#70470 #11790554

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×#70470

Splittings

FittingC2×C32×C4⋊C8 ⋊ C2
SylowC32 ⋊ #1954

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4⋊C8C2
socleC23×C32C22×C4
prime radicalC22×C3×D12C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4⋊C8D3
hypocenterC3C3×#1954
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C8

861 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 24565);