Finite Group Databasebeta

C2×#21425381 #28616542

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21425381

Splittings

FittingC2×C59×#413 ⋊ C2
SylowC59 ⋊ C2×#2050

Subgroups

subgroupG/H
centerC2×C4#14273713
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#413C2
socleC22×C59#394
prime radicalC2×#16838200C2
hypercenterC2×#413D59
hypocenterC59C2×#2050
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

1382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1328 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 197421);