Finite Group Databasebeta

C4×#15688899 #26131100

order12032
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct productC4×#15688899

Splittings

SylowC47 ⋊ C4×#346

Subgroups

subgroupG/H
centerC2×C4×C8C2×D47
commutatorC2×C47C42×C8
FrattiniC22×C8C22×D47
FittingC42×C8×C47C2
socle, prime radicalC23×C47C22×C8
cosocleC22×C8×C47C23
hypercenterC42×C8D47
hypocenterC47C4×#346
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4×C8 ◁ C42×C8

510 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84390);