Finite Group Databasebeta

C2×#20243494 #26216131

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20243494

Splittings

SylowC47 ⋊ C2×#1828

Subgroups

subgroupG/H
centerC22#15688984
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC22×#99×C47C2
socleC22×C47#381
prime radicalC23×D4×C47C22
cosocleC24×C47C24
hypercenterC22×#99D47
hypocenterC47C2×#1828
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

1554 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, 169421);