Finite Group Databasebeta

C2×#10590344 #11860170

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#10590344

Splittings

SylowC32 ⋊ C2×#442

Subgroups

subgroupG/H
centerC23C2×#625
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#442
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

1289 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal quotient of#72222825

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 94181);