Finite Group Databasebeta

#28510249

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C22×C42

Aliases

No aliases for this group.

Splittings

SylowC59 ⋊ #13819

Subgroups

subgroupG/H
center, FrattiniC24C23×D59
commutatorC22×C59C22×C42
FittingC2×C59×#387C2
socle, prime radical, cosocleC24×C59C24
hypercenterC2×#387D59
hypocenterC59#13819
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#387

1514 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Polycyclic presentation:

2^8,59|a^2=g,b^2=h,c^2=g,d^2=efg,b^a=be,c^a=cf,i^a=i^58,d^b=de,i^c=i^58,i^d=i^58

Conjugacy classes & character table

1724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 91128);