Finite Group Databasebeta

← Prev (#26223237) Next (#26223239) →

#123×C47⋊C8 #26223238

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct product#123×C47⋊C8

Splittings

SylowC47 ⋊ C8×#123

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C23×C8
FittingC4×#123×C47C2
socleC23×C47C23×C4
prime radicalC22×D4×C47C2×C4
cosocleC22×C4×C47C24
hypercenterC4×#123D47
hypocenterC47C8×#123
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×#123

1034 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 176528);