Finite Group Databasebeta

D59×#2365 #28748275

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD59×#2365

Splittings

FittingC59×#2365 ⋊ C2
SylowC59 ⋊ C2×#2365

Subgroups

subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingC59×#2365C2
socle, cosocleC23×C59C25
prime radicalC23×D59C24
hypercenter#2365D59
hypocenterC59C2×#2365
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2365

3158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 329154);