Finite Group Databasebeta

#496×Dic47 #26224821

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct product#496×Dic47

Splittings

SylowC47 ⋊ C4×#496

Subgroups

subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#496C2
socleC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC2×#496D47
hypocenterC47C4×#496
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

1262 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 178111);