Finite Group Databasebeta

C2×#20241919 #26183512

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20241919

Splittings

FittingC2×C47×#328 ⋊ C2
SylowC47 ⋊ C2×#1511

Subgroups

subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#328C2
socleC23×C47C2×C22⋊C4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenterC2×#328D47
hypocenterC47C2×#1511
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

1446 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

926 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 136802);