Finite Group Databasebeta

C2×#20243308 #26215426

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20243308

Splittings

FittingC2×C47×#407 ⋊ C2
SylowC47 ⋊ C2×#1783

Subgroups

subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#407C2
socleC23×C47C2×C22⋊C4
prime radicalC24×D188C2
cosocleC22×C4×C47C24
hypercenterC2×#407D47
hypocenterC47C2×#1783
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

5942 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168716);