Finite Group Databasebeta

C4×#15688947 #26131665

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#15688947

Splittings

SylowC47 ⋊ C4×#365

Subgroups

subgroupG/H
centerC2×C4#13093955
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC4×#108×C47C2
socleC22×C47C2×#106
prime radicalC23×C47C2×SD16
cosocleC22×C8×C47C23
hypercenterC4×#108D47
hypocenterC47C4×#365
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#108

330 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84955);