Finite Group Databasebeta

C4×#15688930 #26131502

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#15688930

Splittings

SylowC47 ⋊ C4×#359

Subgroups

subgroupG/H
centerC42#10625334
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC4×#135×C47C2
socleC22×C47C2×#102
prime radicalC2×#135×C47C22
cosocleC22×C8×C47C23
hypercenterC4×#135D47
hypocenterC47C4×#359
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

450 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, 84792);