Finite Group Databasebeta

C2×#20244205 #26219923

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20244205

Splittings

SylowC47 ⋊ C2×#1959

Subgroups

subgroupG/H
centerC24C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#124×C47C2
socleC24×C47C2×D4
prime radicalC23×D4×C47C22
cosocleC22×C4×C47C24
hypercenterC22×#124D47
hypocenterC47C2×#1959
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#124

1814 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 173213);