Finite Group Databasebeta

C2×#20243351 #26215599

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

Aliases

direct productC2×#20243351

Splittings

FittingC2×C47×#408 ⋊ C2
SylowC47 ⋊ C2×#1794

Subgroups

subgroupG/H
centerC2×C4#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#408C2
socleC22×C47#379
prime radicalC2×#15689959C2
cosocleC22×C4×C47C24
hypercenterC2×#408D47
hypocenterC47C2×#1794
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#408

3662 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, 168889);