Finite Group Databasebeta

C22×#14583619 #26003612

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

Aliases

direct productC22×#14583619

Splittings

SylowC43 ⋊ C22×#556

Subgroups

subgroupG/H
centerC24C23×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC22×C4×D4×C43C2
socleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC22×C4×D4D43
hypocenterC43C22×#556
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C4×D4

7846 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, 1076583);