Finite Group Databasebeta

#423×Dic47 #26214182

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct product#423×Dic47

Splittings

SylowC47 ⋊ C4×#423

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C22×C42
FittingC2×C47×#423C2
socleC23×C47C23×C4
prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC2×#423D47
hypocenterC47C4×#423
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#423

1382 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, 167472);