Finite Group Databasebeta

C4×#15688905 #26131318

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#15688905

Splittings

SylowC47 ⋊ C4×#349

Subgroups

subgroupG/H
centerC42C22⋊Dic47
commutatorC22×C47C2×C4×C8
FrattiniC22×C8C22×D47
FittingC2×C4×M16×C47C2
socleC22×C47C2×C22⋊C8
prime radicalC24×C47C2×C8
cosocleC22×C8×C47C23
hypercenterC2×C4×M16D47
hypocenterC47C4×#349
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ C2×C4×M16

522 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84608);