Finite Group Databasebeta

D59×#1392 #28503648

order15104
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD59×#1392

Splittings

FittingC59×#1392 ⋊ C2
SylowC59 ⋊ C2×#1392

Subgroups

subgroupG/H
centerC4#99×D59
commutatorC23×C59C2×C42
FrattiniC2×#41C22×D59
FittingC59×#1392C2
socleC2×C59C2×#342
prime radicalC2×#41×D59C22
cosocleC2×#41×C59C23
hypercenter#1392D59
hypocenterC59C2×#1392
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1392

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84527);