Finite Group Databasebeta

D59×#2285 #28746980

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productD59×#2285

Splittings

FittingC59×#2285 ⋊ C2
SylowC59 ⋊ C2×#2285

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC59×#2285C2
socle, cosocleC23×C59C25
prime radicalC24×D59C23
hypercenter#2285D59
hypocenterC59C2×#2285
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #2285

3854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 327859);