Finite Group Databasebeta

D59×#2916 #29452383

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

Aliases

direct productD59×#2916

Splittings

FittingC59×#2916 ⋊ C2
SylowC59 ⋊ C2×#2916

Subgroups

subgroupG/H
centerC4C22×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC59×#2916C2
socleC2×C59C23×C4⋊C4
prime radicalC2×#41×D59C22
cosocleC2×C4×C59C25
hypercenter#2916D59
hypocenterC59C2×#2916
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C2×#41 ◁ #2916

2586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 1033262);