Finite Group Databasebeta

C4×C59⋊#401 #28510552

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

Aliases

direct productC4×C59⋊#401

Splittings

SylowC59 ⋊ C4×#401

Subgroups

subgroupG/H
centerC23×C4C22×D59
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC4×#95×C59C2
socle, prime radical, cosocleC24×C59C24
hypercenterC4×#95D59
hypocenterC59C4×#401
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23×C4 ◁ C4×#95

1222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 91431);