Finite Group Databasebeta

C23×#14273717 #29495355

order15104
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC23×#14273717

Splittings

SylowC59 ⋊ C23×#125

Subgroups

subgroupG/H
centerC25C22×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC23×C4⋊C4×C59C2
socle, prime radicalC25×C59C23
hypercenterC23×C4⋊C4D59
hypocenterC59C23×#125
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C25 ◁ C23×C4⋊C4

8414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076234);