Finite Group Databasebeta

C4×#15689532 #26225090

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC4×#15689532

Splittings

SylowC47 ⋊ C4×#501

Subgroups

subgroupG/H
centerC22×C4C2×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#97×C47C2
socle, prime radicalC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC4×#97D47
hypocenterC47C4×#501
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#97

802 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 178380);