Finite Group Databasebeta

C2×#20251784 #26422374

order12032
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#20251784

Splittings

SylowC47 ⋊ C2×#2868

Subgroups

subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC22×C4⋊Q8×C47C2
socle, prime radicalC24×C47C24
hypercenterC22×C4⋊Q8D47
hypocenterC47C2×#2868
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

3774 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 375664);