Finite Group Databasebeta

C2×#19138226 #25265024

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19138226

Splittings

FittingC22×#124×C43 ⋊ C2
SylowC43 ⋊ C2×#2432

Subgroups

subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#124×C43C2
socleC24×C43C24
prime radicalC23×#10621900C2
hypercenterC22×#124D43
hypocenterC43C2×#2432
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#124

5502 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 337995);