Finite Group Databasebeta

D59×#2358 #28748174

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD59×#2358

Splittings

FittingC59×#2358 ⋊ C2
SylowC59 ⋊ C2×#2358

Subgroups

subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingC59×#2358C2
socle, cosocleC23×C59C25
prime radicalC2×#120×D59C2
hypercenter#2358D59
hypocenterC59C2×#2358
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2358

5942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 329053);