Finite Group Databasebeta

C2×#99×Dic59 #28586337

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#99×Dic59

Splittings

SylowC59 ⋊ C2×C4×#99

Subgroups

subgroupG/H
centerC23C22⋊C4×D59
commutatorC22×C59C22×C42
FrattiniC24C23×D59
FittingC22×#99×C59C2
socleC23×C59C2×C22⋊C4
prime radicalC23×D4×C59C22
cosocleC24×C59C24
hypercenterC22×#99D59
hypocenterC59C2×C4×#99
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

2242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 167216);