Finite Group Databasebeta

C22×#14583716 #26010423

order11008
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×#14583716

Splittings

FittingC22×#131×C43 ⋊ C2
SylowC43 ⋊ C22×#578

Subgroups

subgroupG/H
centerC23C22×D172
commutator, cosocleC4×C43C26
FrattiniC4C25×D43
FittingC22×#131×C43C2
socleC23×C43C22×D4
hypercenterC22×#131D43
hypocenterC43C22×#578
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×#131

10774 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1083394);