Finite Group Databasebeta

C22×#15688905 #26368964

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#15688905

Splittings

SylowC47 ⋊ C22×#349

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic47
commutatorC22×C47C23×C8
FrattiniC2×C8C23×D47
FittingC23×M16×C47C2
socleC23×C47C22⋊C8
prime radicalC25×C47C8
cosocleC2×C8×C47C24
hypercenterC23×M16D47
hypocenterC47C22×#349
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C23×M16

1262 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322254);