Finite Group Databasebeta

C2×#19135591 #25123379

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

Aliases

direct productC2×#19135591

Splittings

FittingC22×#121×C43 ⋊ C2
SylowC43 ⋊ C2×#1999

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#121×C43C2
socleC24×C43C2×D4
hypercenterC22×#121D43
hypocenterC43C2×#1999
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#121

2870 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 196350);