Finite Group Databasebeta

C4×#15689743 #26375404

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

Aliases

direct productC4×#15689743

Splittings

FittingC4×C22⋊Q8×C47 ⋊ C2
SylowC47 ⋊ C4×#542

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC4×C22⋊Q8×C47C2
socle, cosocleC23×C47C25
prime radicalC2×#13093997C22
hypercenterC4×C22⋊Q8D47
hypocenterC47C4×#542
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

2294 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328694);