Finite Group Databasebeta

C4×#15688926 #26131490

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

Aliases

direct productC4×#15688926

Splittings

SylowC47 ⋊ C4×#358

Subgroups

subgroupG/H
centerC22×C4#10625334
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC4×#107×C47C2
socle, prime radicalC23×C47C2×D8
cosocleC22×C8×C47C23
hypercenterC4×#107D47
hypocenterC47C4×#358
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#107

470 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, 84780);