Finite Group Databasebeta

C2×C3×#4690 #11858771

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

Aliases

direct productC2×C3×#4690

Splittings

FittingC2×C32×C4×C8 ⋊ C2
SylowC32 ⋊ C2×#433

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4×C8C2
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×C4×C8D3
hypocenterC3C2×C3×#433
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×C8

905 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 92782);