Finite Group Databasebeta

C2×#20241472 #26131137

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241472

Splittings

SylowC47 ⋊ C2×#1377

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic47
commutatorC22×C47C2×C4×C8
FrattiniC22×C8C22×D47
FittingC22×#97×C47C2
socleC23×C47C22⋊C8
prime radicalC24×C47C2×C8
cosocleC22×C8×C47C23
hypercenterC22×#97D47
hypocenterC47C2×#1377
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×#97

630 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, 84427);