Finite Group Databasebeta

C2×#20246081 #26375032

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#20246081

Splittings

FittingC22×#117×C47 ⋊ C2
SylowC47 ⋊ C2×#2324

Subgroups

subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC22×#117×C47C2
socleC24×C47C24
prime radicalC22×#13093998C2
cosocleC23×C47C25
hypercenterC22×#117D47
hypocenterC47C2×#2324
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#117

3934 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328322);