Finite Group Databasebeta

C4×#15689172 #26214385

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#15689172

Splittings

SylowC47 ⋊ C4×#430

Subgroups

subgroupG/H
centerC42C2×D188
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC2×C4×M16×C47C2
socleC22×C47C22×C4⋊C4
prime radicalC24×C47C2×Q8
cosocleC22×C4×C47C24
hypercenterC2×C4×M16D47
hypocenterC47C4×#430
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×C4×M16

1034 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, 167675);