Finite Group Databasebeta

C2×#20243677 #26217393

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20243677

Splittings

FittingC22×C22⋊C8×C47 ⋊ C2
SylowC47 ⋊ C2×#1869

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C23×C8
FrattiniC22×C4C23×D47
FittingC22×C22⋊C8×C47C2
socleC24×C47C22×C4
prime radicalC23×C22⋊D47C4
cosocleC22×C4×C47C24
hypercenterC22×C22⋊C8D47
hypocenterC47C2×#1869
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

2438 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 170683);