Finite Group Databasebeta

C4×#15689553 #26369558

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#15689553

Splittings

FittingC4×#135×C47 ⋊ C2
SylowC47 ⋊ C4×#508

Subgroups

subgroupG/H
centerC42#10625334
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC4×#135×C47C2
socleC22×C47C22×D8
prime radicalC2×#15689553C2
cosocleC2×C8×C47C24
hypercenterC4×#135D47
hypocenterC47C4×#508
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

690 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, 322848);