Finite Group Databasebeta

C2×#20243495 #26216132

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

Aliases

direct productC2×#20243495

Splittings

FittingC2×C47×#342 ⋊ C2
SylowC47 ⋊ C2×#1828

Subgroups

subgroupG/H
centerC22#15688985
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC2×C47×#342C2
socleC22×C47#381
prime radicalC23×C22⋊D47C22
cosocleC24×C47C24
hypercenterC2×#342D47
hypocenterC47C2×#1828
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

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, 169422);