Finite Group Databasebeta

C3×#69285 #11797013

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

Aliases

direct productC3×#69285

Splittings

FittingC32×C4⋊C16 ⋊ C2
SylowC32 ⋊ #2151

Subgroups

subgroupG/H
centerC2×C3×C8C22×D3
commutatorC22×C3C22×C3×C8
FrattiniC2×C8C22×C3×D3
FittingC32×C4⋊C16C2
socleC22×C32C22×C8
prime radicalC22×C3×D3C2×C8
cosocleC2×C3×C8C23×C3
hypercenterC3×C4⋊C16D3
hypocenterC3C3×#2151
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C8 ◁ C3×C4⋊C16

345 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, 31024);