Finite Group Databasebeta

#117×D188 #26375684

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct product#117×D188

Splittings

FittingC4×#117×C47 ⋊ C2
SylowC47 ⋊ D4×#117

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC4×#117×C47C2
socle, cosocleC23×C47C25
prime radicalC23×D188C22
hypercenterC4×#117D47
hypocenterC47D4×#117
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×#117

3562 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328974);