Finite Group Databasebeta

C2×#19137637 #25256154

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#19137637

Splittings

SylowC43 ⋊ C2×#2363

Subgroups

subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
Fitting, prime radicalC22×#121×C43C2
socleC24×C43C24
cosocleC23×C43C25
hypercenterC22×#121D43
hypocenterC43C2×#2363
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#121

4046 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 329125);