Finite Group Databasebeta

C2×#117×Dic47 #26374465

order12032
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×#117×Dic47

Splittings

SylowC47 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC22×#117×C47C2
socleC24×C47C24
prime radicalC25×C47C23
cosocleC23×C47C25
hypercenterC22×#117D47
hypocenterC47C2×C4×#117
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×#117

4462 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327755);