Finite Group Databasebeta

C2×#10588136 #11774171

order1152
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#10588136

Splittings

FittingC2×C4×C8×C9 ⋊ C2
SylowC9 ⋊ C2×D4⋊C8

Subgroups

subgroupG/H
centerC22×C4D36
commutatorC4×C9C22×C8
FrattiniC3×C42C22×D3
FittingC2×C4×C8×C9C2
socleC23×C3(C2×D3)⋊C4
prime radicalC22×D36C4
cosocleC42×C9C23
hypercenterC2×C4×C8D9
hypocenterC9C2×D4⋊C8
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

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, 8182);