Finite Group Databasebeta

C2×#19135728 #25123864

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

Aliases

direct productC2×#19135728

Splittings

FittingC22×C4⋊Q8×C43 ⋊ C2
SylowC43 ⋊ C2×#2023

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×C4⋊Q8×C43C2
socleC24×C43C2×D4
prime radicalC23×D172C22
hypercenterC22×C4⋊Q8D43
hypocenterC43C2×#2023
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊Q8

1734 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, 196835);