Finite Group Databasebeta

C2×#19136537 #25250368

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

Aliases

direct productC2×#19136537

Splittings

FittingC2×C43×C22⋊C16 ⋊ C2
SylowC43 ⋊ C2×#2189

Subgroups

subgroupG/H
centerC23C2×D344
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×C22⋊C16C2
socleC23×C43C2×D8
prime radicalC22×#13063347C2
hypercenterC2×C22⋊C16D43
hypocenterC43C2×#2189
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

1146 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, 323339);