Finite Group Databasebeta

C4×#15689107 #26213955

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#15689107

Splittings

SylowC47 ⋊ C4×#413

Subgroups

subgroupG/H
centerC42C22⋊Dic47
commutatorC22×C47C22×C42
FrattiniC22×C4C23×D47
FittingC2×C4×#41×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC2×C4×#41D47
hypocenterC47C4×#413
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×C4×#41

1570 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, 167245);