Finite Group Databasebeta

#444×Dic47 #26214852

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

Aliases

direct product#444×Dic47

Splittings

SylowC47 ⋊ C4×#444

Subgroups

subgroupG/H
centerC2×C4C2×D4×D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC2×C47×#444C2
socleC22×C47C2×C4×D4
prime radicalC2×#135×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#444D47
hypocenterC47C4×#444
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#444

1022 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, 168142);