Finite Group Databasebeta

C2×C3×#4907 #11899385

order1152
automorphism?
homologyAbelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×C3×#4907

Splittings

FittingC2×C32×M32 ⋊ C2
SylowC32 ⋊ C2×#504

Subgroups

subgroupG/H
centerC2×C3×C8C22×D3
commutatorC2×C3C23×C3×C8
FrattiniC8C23×C3×D3
FittingC2×C32×M32C2
socleC22×C32C22×C8
prime radicalC2×C3×#235C4
cosocleC3×C8C24×C3
hypercenterC2×C3×M32D3
hypocenterC3C2×C3×#504
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C8 ◁ C2×C3×M32

781 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

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, 133396);