Finite Group Databasebeta

C22×#15688938 #26369232

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#15688938

Splittings

SylowC47 ⋊ C22×#362

Subgroups

subgroupG/H
centerC23#13093944
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC22×#108×C47C2
socleC23×C47#102
prime radicalC24×C47SD16
cosocleC2×C8×C47C24
hypercenterC22×#108D47
hypocenterC47C22×#362
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#108

1134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322522);