Finite Group Databasebeta

C2×#20241235 #26105926

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20241235

Splittings

SylowC47 ⋊ C2×#1282

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic47
commutatorC22×C47C2×C4×C8
FrattiniC23×C4C22×D47
FittingC22×C22⋊C8×C47C2
socleC23×C47#95
prime radicalC25×C47C2×C4
cosocleC23×C4×C47C23
hypercenterC22×C22⋊C8D47
hypocenterC47C2×#1282
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×C22⋊C8

1130 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 59216);