Finite Group Databasebeta

C2×#20241311 #26125336

order12032
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241311

Splittings

FittingC2×C47×C22⋊C16 ⋊ C2
SylowC47 ⋊ C2×#1314

Subgroups

subgroupG/H
centerC22×C4(C2×D47)⋊C4
commutatorC22×C47C22×C16
FrattiniC22×C8C22×D47
FittingC2×C47×C22⋊C16C2
socleC23×C47C22⋊C8
prime radicalC24×D47C8
cosocleC22×C8×C47C23
hypercenterC2×C22⋊C16D47
hypocenterC47C2×#1314
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C2×C22⋊C16

682 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, 78626);