Finite Group Databasebeta

C2×#10588403 #11869486

order1152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#10588403

Splittings

SylowC9 ⋊ C2×#485

Subgroups

subgroupG/H
centerC23C2×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC2×C9×C22⋊C8C2
socleC23×C3C2×D12
prime radicalC24×C3D12
hypercenterC2×C22⋊C8D9
hypocenterC9C2×#485
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 103497);