Finite Group Databasebeta

#349×Dic47 #26131320

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#349×Dic47

Splittings

SylowC47 ⋊ C4×#349

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C2×C4×C8
FrattiniC22×C8C22×D47
FittingC2×C47×#349C2
socleC22×C47C2×C22⋊C8
prime radicalC24×C47C2×C8
cosocleC22×C8×C47C23
hypercenterC2×#349D47
hypocenterC47C4×#349
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#349

522 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, 84610);