Finite Group Databasebeta

C2×#19135726 #25123835

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135726

Splittings

FittingC2×C43×#381 ⋊ C2
SylowC43 ⋊ C2×#2022

Subgroups

subgroupG/H
centerC23#13063293
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC2×C43×#381C2
socleC23×C43#120
prime radicalC2×#14583461C2
hypercenterC2×#381D43
hypocenterC43C2×#2022
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#381

2394 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 196806);