Finite Group Databasebeta

C2×#20241324 #26125397

order12032
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20241324

Splittings

SylowC47 ⋊ C2×#1320

Subgroups

subgroupG/H
centerC2×C4#13093939
commutatorC23×C47C22×C8
FrattiniC2×M16C22×D47
FittingC2×C47×#407C2
socleC22×C47#323
prime radicalC25×C47C8
cosocleC2×M16×C47C23
hypercenterC2×#407D47
hypocenterC47C2×#1320
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#407

626 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 78687);