Finite Group Databasebeta

C2×#19137319 #25255399

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×#19137319

Splittings

FittingC2×C43×#390 ⋊ C2
SylowC43 ⋊ C2×#2328

Subgroups

subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#390C2
socleC24×C43C24
prime radicalC22×#13063321C2
cosocleC23×C43C25
hypercenterC2×#390D43
hypocenterC43C2×#2328
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#390

4430 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328370);