Finite Group Databasebeta

C2×#10588359 #11861284

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#10588359

Splittings

SylowC9 ⋊ C2×#446

Subgroups

subgroupG/H
centerC22×C4C22×D9
commutatorC22×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC2×C4×C8×C9C2
socle, prime radicalC23×C3C2×C4×D3
cosocleC2×C4×C9C24
hypercenterC2×C4×C8D9
hypocenterC9C2×#446
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×C4×C8

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 95295);