Finite Group Databasebeta

C2×#20243921 #26218271

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20243921

Splittings

SylowC47 ⋊ C2×#1911

Subgroups

subgroupG/H
centerC22#15689003
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#535C2
socleC22×C47#386
cosocleC22×C4×C47C24
hypercenterC2×#535D47
hypocenterC47C2×#1911
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#535

1974 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 171561);