Finite Group Databasebeta

C2×#20241454 #26127830

order12032
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20241454

Splittings

SylowC47 ⋊ C2×#1368

Subgroups

subgroupG/H
centerC23#13093956
commutatorC8×C47C22×C8
FrattiniC4×C8C22×D47
FittingC2×C47×#346C2
socle, prime radicalC23×C47#106
cosocleC4×C8×C47C23
hypercenterC2×#346D47
hypocenterC47C2×#1368
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#346

254 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 81120);