Finite Group Databasebeta

C2×#10590788 #11861314

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

Aliases

direct productC2×#10590788

Splittings

SylowC32 ⋊ C2×#446

Subgroups

subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socle, prime radicalC23×C32C22×C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#446
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

881 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 95325);