Finite Group Databasebeta

C2×#20241268 #26106263

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20241268

Splittings

SylowC47 ⋊ C2×#1294

Subgroups

subgroupG/H
centerC24(C2×D47)⋊C4
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC22×C22⋊C8×C47C2
socleC24×C47C22⋊C4
prime radicalC25×C47D4
cosocleC23×C4×C47C23
hypercenterC22×C22⋊C8D47
hypocenterC47C2×#1294
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

1454 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 59553);