Finite Group Databasebeta

C2×#20243940 #26218307

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

Aliases

direct productC2×#20243940

Splittings

SylowC47 ⋊ C2×#1915

Subgroups

subgroupG/H
centerC22#15689002
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#568C2
socleC22×C47#386
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#568D47
hypocenterC47C2×#1915
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#568

1670 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1622 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 171597);