Finite Group Databasebeta

C2×#20243113 #26213697

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20243113

Splittings

FittingC2×C47×#341 ⋊ C2
SylowC47 ⋊ C2×#1738

Subgroups

subgroupG/H
centerC22×C4D4×D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC2×C47×#341C2
socleC23×C47C2×C4⋊C4
prime radicalC24×D47Q8
cosocleC22×C4×C47C24
hypercenterC2×#341D47
hypocenterC47C2×#1738
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#341

2110 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 166987);