Finite Group Databasebeta

C22×#14583575 #26003573

order11008
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×#14583575

Splittings

FittingC23×C22⋊C4×C43 ⋊ C2
SylowC43 ⋊ C22×#551

Subgroups

subgroupG/H
centerC24C23×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC23×C22⋊C4×C43C2
socleC24×C43C24
prime radicalC22×#13063294C2
hypercenterC23×C22⋊C4D43
hypocenterC43C22×#551
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C22⋊C4

9526 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076544);