Finite Group Databasebeta

C2×#20247508 #26383852

order12032
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#20247508

Splittings

FittingC23×C22⋊C4×C47 ⋊ C2
SylowC47 ⋊ C2×#2472

Subgroups

subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC23×C22⋊C4×C47C2
socleC24×C47C24
prime radicalC22×#13093993C2
hypercenterC23×C22⋊C4D47
hypocenterC47C2×#2472
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C22⋊C4

4946 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 337142);