Finite Group Databasebeta

C2×#20241365 #26126070

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

Aliases

direct productC2×#20241365

Splittings

FittingC2×C47×#322 ⋊ C2
SylowC47 ⋊ C2×#1336

Subgroups

subgroupG/H
centerC2×C4#13093946
commutatorC8×C47C22×C8
FrattiniC4×C8C22×D47
FittingC2×C47×#322C2
socleC22×C47D4⋊C8
prime radicalC2×#13094046C4
cosocleC4×C8×C47C23
hypercenterC2×#322D47
hypocenterC47C2×#1336
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×#322

398 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, 79360);