Finite Group Databasebeta

C2×C3×#67⋊C8 #11859146

order1152
automorphism?
homologyAbelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×#67⋊C8

Splittings

FittingC2×C32×C22⋊C8 ⋊ C2
SylowC32 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutatorC2×C3C23×C3×C8
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C22×C4
prime radicalC22×C3×#67C4
cosocleC2×C3×C4C24×C3
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C2×C3×C8×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C22⋊C8

1333 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, 93157);