Finite Group Databasebeta

#359×Dic47 #26131504

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#359×Dic47

Splittings

SylowC47 ⋊ C4×#359

Subgroups

subgroupG/H
centerC2×C4D8×D47
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC2×C47×#359C2
socleC22×C47C2×#102
prime radicalC2×#135×C47C22
cosocleC22×C8×C47C23
hypercenterC2×#359D47
hypocenterC47C4×#359
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

450 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84794);