Finite Group Databasebeta

C2×#20243339 #26215554

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

Aliases

direct productC2×#20243339

Splittings

SylowC47 ⋊ C2×#1791

Subgroups

subgroupG/H
centerC2×C4#13093993
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#585C2
socleC22×C47#379
cosocleC22×C4×C47C24
hypercenterC2×#585D47
hypocenterC47C2×#1791
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#585

3662 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168844);