Finite Group Databasebeta

C2×#20243529 #26216508

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20243529

Splittings

SylowC47 ⋊ C2×#1838

Subgroups

subgroupG/H
centerC22×C4C2×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#97×C47C2
socleC23×C47C2×C4⋊C4
prime radicalC24×C47C2×Q8
cosocleC22×C4×C47C24
hypercenterC22×#97D47
hypocenterC47C2×#1838
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×#97

830 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, 169798);