Finite Group Databasebeta

D59×#1280 #28478275

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productD59×#1280

Splittings

FittingC59×#1280 ⋊ C2
SylowC59 ⋊ C2×#1280

Subgroups

subgroupG/H
centerC23C22⋊C4×D59
commutatorC22×C59C2×C4×C8
FrattiniC23×C4C22×D59
FittingC59×#1280C2
socleC23×C59C2×C22⋊C4
prime radicalC24×D59C2×C4
cosocleC23×C4×C59C23
hypercenter#1280D59
hypocenterC59C2×#1280
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

1390 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, 59154);