Finite Group Databasebeta

#400×Dic59 #28510539

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

Aliases

direct product#400×Dic59

Splittings

SylowC59 ⋊ C4×#400

Subgroups

subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#400C2
socle, prime radical, cosocleC24×C59C24
hypercenterC2×#400D59
hypocenterC59C4×#400
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#400

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

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, 91418);