Finite Group Databasebeta

C4×#15688887 #26121464

order12032
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct productC4×#15688887

Splittings

SylowC47 ⋊ C4×#341

Subgroups

subgroupG/H
centerC2×C42C22⋊D47
commutatorC4×C47C43
FrattiniC23×C4C22×D47
FittingC2×C4×M16×C47C2
socleC23×C47C2×C4⋊C4
prime radicalC24×C47C2×Q8
cosocleC23×C4×C47C23
hypercenterC2×C4×M16D47
hypocenterC47C4×#341
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×C4×M16

910 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 74754);