Finite Group Databasebeta

C2×#20241231 #26105866

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20241231

Splittings

SylowC47 ⋊ C2×#1280

Subgroups

subgroupG/H
centerC24C22⋊Dic47
commutatorC22×C47C2×C4×C8
FrattiniC23×C4C22×D47
FittingC22×#95×C47C2
socleC24×C47C22⋊C4
prime radicalC25×C47C2×C4
cosocleC23×C4×C47C23
hypercenterC22×#95D47
hypocenterC47C2×#1280
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#95

1390 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, 59156);