Finite Group Databasebeta

C2×#19136520 #25250360

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

Aliases

direct productC2×#19136520

Splittings

FittingC2×C43×C22⋊C16 ⋊ C2
SylowC43 ⋊ C2×#2186

Subgroups

subgroupG/H
centerC23C2×D344
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×C22⋊C16C2
socleC23×C43C2×D8
hypercenterC2×C22⋊C16D43
hypocenterC43C2×#2186
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

1198 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1738 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 323331);