Finite Group Databasebeta

C2×#20243119 #26213708

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#20243119

Splittings

SylowC47 ⋊ C2×#1740

Subgroups

subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC2×C47×#342C2
socleC23×C47C2×C22⋊C4
prime radicalC25×C47C23
cosocleC24×C47C24
hypercenterC2×#342D47
hypocenterC47C2×#1740
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

2350 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 166998);