Finite Group Databasebeta

C2×#124×Dic47 #26374752

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

Aliases

direct productC2×#124×Dic47

Splittings

SylowC47 ⋊ C2×C4×#124

Subgroups

subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC22×#124×C47C2
socleC24×C47C24
prime radicalC23×D4×C47C22
cosocleC23×C47C25
hypercenterC22×#124D47
hypocenterC47C2×C4×#124
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#124

3790 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328042);