Finite Group Databasebeta

C2×#20241701 #26182071

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20241701

Splittings

FittingC2×C47×#324 ⋊ C2
SylowC47 ⋊ C2×#1458

Subgroups

subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C47C23×C8
FrattiniC22×C4C23×D47
FittingC2×C47×#324C2
socleC23×C47C2×C22⋊C4
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenterC2×#324D47
hypocenterC47C2×#1458
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

1390 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 135361);