Finite Group Databasebeta

D59×#1496 #28555305

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD59×#1496

Splittings

FittingC59×#1496 ⋊ C2
SylowC59 ⋊ C2×#1496

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#1496C2
socleC22×C59C22×C22⋊C4
prime radical#532×D59C2
cosocleC42×C59C24
hypercenter#1496D59
hypocenterC59C2×#1496
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

1270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 136184);