Finite Group Databasebeta

C2×#19137788 #25259261

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

Aliases

direct productC2×#19137788

Splittings

FittingC2×C43×#384 ⋊ C2
SylowC43 ⋊ C2×#2383

Subgroups

subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#384C2
socleC24×C43C24
prime radicalC24×D43C23
cosocleC23×C43C25
hypercenterC2×#384D43
hypocenterC43C2×#2383
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#384

2502 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, 332232);