Finite Group Databasebeta

C2×#10592639 #11801407

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3×C4

Aliases

direct productC2×#10592639

Splittings

FittingC22×C32×C42 ⋊ C2
SylowC32 ⋊ C2×#388

Subgroups

subgroupG/H
centerC24C22×C3⋊D3
commutatorC22×C32C23×C4
FrattiniC23C23×C3⋊D3
FittingC22×C32×C42C2
socleC24×C32C23
prime radicalC24×C3⋊D3C22
cosocleC23×C32C24
hypercenterC22×C42C3⋊D3
hypocenterC32C2×#388
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C22×C42

2784 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, 35418);