Finite Group Databasebeta

C2×#20243317 #26215456

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20243317

Splittings

FittingC22×#102×C47 ⋊ C2
SylowC47 ⋊ C2×#1786

Subgroups

subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#102×C47C2
socleC24×C47C2×D4
prime radicalC23×D4×D47C2
cosocleC22×C4×C47C24
hypercenterC22×#102D47
hypocenterC47C2×#1786
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

6086 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168746);