Finite Group Databasebeta

C2×#21421962 #28478530

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21421962

Splittings

SylowC59 ⋊ C2×#1288

Subgroups

subgroupG/H
centerC23C59⋊#95
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC2×C59×#432C2
socleC23×C59#95
prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenterC2×#432D59
hypocenterC59C2×#1288
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 59409);