Finite Group Databasebeta

C2×#20244786 #26244995

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20244786

Splittings

SylowC47 ⋊ C2×#2069

Subgroups

subgroupG/H
centerC22#15689046
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#100×C47C2
socleC22×C47#396
prime radicalC23×D4×C47C22
hypercenterC22×#100D47
hypocenterC47C2×#2069
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#100

1078 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1058 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 198285);