Finite Group Databasebeta

D59×#1461 #28554493

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productD59×#1461

Splittings

FittingC59×#1461 ⋊ C2
SylowC59 ⋊ C2×#1461

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D59
commutatorC22×C59C23×C8
FrattiniC22×C4C23×D59
FittingC59×#1461C2
socleC22×C59C22×C22⋊C4
prime radicalC23×D59C22×C4
cosocleC22×C4×C59C24
hypercenter#1461D59
hypocenterC59C2×#1461
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

1282 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, 135372);