Finite Group Databasebeta

C2×#20243369 #26215634

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

Aliases

direct productC2×#20243369

Splittings

FittingC22×C4⋊C8×C47 ⋊ C2
SylowC47 ⋊ C2×#1798

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×C4⋊C8×C47C2
socleC24×C47C22×C4
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenterC22×C4⋊C8D47
hypocenterC47C2×#1798
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

1638 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, 168924);