Finite Group Databasebeta

#520×Dic59 #28746934

order15104
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct product#520×Dic59

Splittings

SylowC59 ⋊ C4×#520

Subgroups

subgroupG/H
center, FrattiniC23C24×D59
commutatorC2×C59C23×C42
FittingC2×C59×#520C2
socle, cosocleC23×C59C25
prime radicalC22×#41×C59C22
hypercenterC2×#520D59
hypocenterC59C4×#520
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#520

3698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 327813);