Finite Group Databasebeta

C2×#20243349 #26215570

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20243349

Splittings

FittingC22×#101×C47 ⋊ C2
SylowC47 ⋊ C2×#1793

Subgroups

subgroupG/H
centerC23#13093994
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#101×C47C2
socleC23×C47#120
prime radicalC22×#13094072C2
cosocleC22×C4×C47C24
hypercenterC22×#101D47
hypocenterC47C2×#1793
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

3682 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168860);