Finite Group Databasebeta

C4×#15688845 #26105627

order12032
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C43

Aliases

direct productC4×#15688845

Splittings

SylowC47 ⋊ C4×#322

Subgroups

subgroupG/H
centerC43C2×D47
commutatorC2×C47C42×C8
FrattiniC2×C42C22×D47
FittingC42×C8×C47C2
socle, prime radicalC23×C47C2×C42
cosocleC2×C42×C47C23
hypercenterC42×C8D47
hypocenterC47C4×#322
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C43 ◁ C42×C8

654 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, 58917);