Finite Group Databasebeta

C3×#70949 #11798023

order1152
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C2

Aliases

direct productC3×#70949

Splittings

SylowC32 ⋊ #2183

Subgroups

subgroupG/H
centerC2×C3×C8C22×D3
commutatorC22×C3C22×C3×C8
FrattiniC2×C8C22×C3×D3
FittingC32×C8×Q8C2
socle, prime radicalC22×C32C22×C8
cosocleC2×C3×C8C23×C3
hypercenterC3×C8×Q8D3
hypocenterC3C3×#2183
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C8 ◁ C3×C8×Q8

303 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, 32034);