Finite Group Databasebeta

← Prev (#26375336) Next (#26375338) →

C4×#15689704 #26375337

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

Aliases

direct productC4×#15689704

Splittings

FittingC2×C4×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ C4×#537

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C4×C4⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC2×#15689704C2
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C4×#537
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

3186 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328627);