Finite Group Databasebeta

C4×#15689635 #26374743

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#15689635

Splittings

FittingC4×#117×C47 ⋊ C2
SylowC47 ⋊ C4×#525

Subgroups

subgroupG/H
centerC2×C42C22×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC4×#117×C47C2
socle, cosocleC23×C47C25
prime radicalC2×#15689635C2
hypercenterC4×#117D47
hypocenterC47C4×#525
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C4×#117

3902 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328033);