Finite Group Databasebeta

C2×#20243448 #26215953

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20243448

Splittings

FittingC22×#106×C47 ⋊ C2
SylowC47 ⋊ C2×#1815

Subgroups

subgroupG/H
centerC23#13093995
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#106×C47C2
socleC23×C47#121
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC22×#106D47
hypocenterC47C2×#1815
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

1374 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 169243);