Finite Group Databasebeta

← Prev (#26213746) Next (#26213748) →

C2×#20243139 #26213747

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20243139

Splittings

SylowC47 ⋊ C2×#1746

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C22×C42
FrattiniC22×C4C23×D47
FittingC22×C4×C8×C47C2
socle, prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C2×#1746
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×C4×C8

1134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167037);