Finite Group Databasebeta

C2×#10590989 #11867892

order1152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#10590989

Splittings

SylowC32 ⋊ C2×#471

Subgroups

subgroupG/H
centerC22#63910
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#63830C2
hypercenterC2×M16D32
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

1065 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 101903);