Finite Group Databasebeta

C4×#15689657 #26374784

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#15689657

Splittings

FittingC2×C43×C47 ⋊ C2
SylowC47 ⋊ C4×#529

Subgroups

subgroupG/H
centerC2×C42C22×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C43×C47C2
socle, cosocleC23×C47C25
prime radicalC2×#13093998C22
hypercenterC2×C43D47
hypocenterC47C4×#529
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C2×C43

2670 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328074);