Finite Group Databasebeta

C4×#41×Dic47 #26374480

order12032
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#41×Dic47

Splittings

SylowC47 ⋊ C42×#41

Subgroups

subgroupG/H
centerC2×C42C22×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC2×C4×#41×C47C2
socle, cosocleC23×C47C25
prime radicalC22×#41×C47C22
hypercenterC2×C4×#41D47
hypocenterC47C42×#41
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C2×C4×#41

4086 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327770);