Finite Group Databasebeta

C2×#19136535 #25250366

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19136535

Splittings

SylowC43 ⋊ C2×#2189

Subgroups

subgroupG/H
centerC23C2×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
Fitting, prime radicalC22×#135×C43C2
socleC23×C43C2×D8
hypercenterC22×#135D43
hypocenterC43C2×#2189
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#135

1146 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1234 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 323337);