Finite Group Databasebeta

C2×#20241468 #26131125

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

Aliases

direct productC2×#20241468

Splittings

SylowC47 ⋊ C2×#1375

Subgroups

subgroupG/H
centerC22×C4C4×Dic47
commutatorC4×C47C2×C4×C8
FrattiniC22×C8C22×D47
FittingC22×#97×C47C2
socleC23×C47#97
prime radicalC24×C47M16
cosocleC22×C8×C47C23
hypercenterC22×#97D47
hypocenterC47C2×#1375
LCSG ▷ C4×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ 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, 84415);