Finite Group Databasebeta

#344×Dic47 #26121485

order12032
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct product#344×Dic47

Splittings

SylowC47 ⋊ C4×#344

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C43
FrattiniC23×C4C22×D47
FittingC2×C47×#344C2
socleC22×C47C2×#95
prime radicalC24×C47C22×C4
cosocleC23×C4×C47C23
hypercenterC2×#344D47
hypocenterC47C4×#344
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

906 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, 74775);