Finite Group Databasebeta

C2×#20243763 #26217775

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20243763

Splittings

FittingC2×C47×#343 ⋊ C2
SylowC47 ⋊ C2×#1883

Subgroups

subgroupG/H
centerC23#13093994
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#343C2
socleC23×C47#120
prime radicalC22×#13094052C2
cosocleC22×C4×C47C24
hypercenterC2×#343D47
hypocenterC47C2×#1883
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

2018 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 171065);