Finite Group Databasebeta

#585×Dic59 #29495304

order15104
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct product#585×Dic59

Splittings

SylowC59 ⋊ C4×#585

Subgroups

subgroupG/H
centerC2×C4C24×D59
commutatorC2×C59C25×C4
FrattiniC22C25×D59
Fitting, prime radicalC2×C59×#585C2
socle, cosocleC22×C59C26
hypercenterC2×#585D59
hypocenterC59C4×#585
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×#585

11346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076183);