Finite Group Databasebeta

C2×#20242639 #26192081

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20242639

Splittings

FittingC2×C47×Q8⋊C8 ⋊ C2
SylowC47 ⋊ C2×#1649

Subgroups

subgroupG/H
centerC23#13093994
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC2×C47×Q8⋊C8C2
socleC23×C47#120
prime radicalC22×D188D4
hypercenterC2×Q8⋊C8D47
hypocenterC47C2×#1649
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

1206 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 145371);