Finite Group Databasebeta

C2×#20241217 #26105674

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C42

Aliases

direct productC2×#20241217

Splittings

SylowC47 ⋊ C2×#1274

Subgroups

subgroupG/H
centerC22×C4C4×Dic47
commutatorC4×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC2×C47×#376C2
socleC23×C47#95
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#376D47
hypocenterC47C2×#1274
LCSG ▷ C4×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#376

758 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, 58964);