Finite Group Databasebeta

C2×#20243249 #26214205

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20243249

Splittings

SylowC47 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC2×C47×#336C2
socle, prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC2×#336D47
hypocenterC47C2×C8×C4⋊C4
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×#336

1438 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167495);