Finite Group Databasebeta

C2×#19137852 #25262837

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19137852

Splittings

FittingC22×#117×C43 ⋊ C2
SylowC43 ⋊ C2×#2395

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#117×C43C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC22×#117D43
hypocenterC43C2×#2395
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×#117

3182 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 335808);