Finite Group Databasebeta

C2×#20247585 #26384709

order12032
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#20247585

Splittings

FittingC22×C22⋊Q8×C47 ⋊ C2
SylowC47 ⋊ C2×#2477

Subgroups

subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC22×C22⋊Q8×C47C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC22×C22⋊Q8D47
hypocenterC47C2×#2477
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

3070 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 337999);