Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | D59×#2639 |
| Fitting | C59×#2639 ⋊ C2 |
| Sylow | C59 ⋊ C2×#2639 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D59 |
| commutator, socle, cosocle | C23×C59 | C25 |
| Fitting | C59×#2639 | C2 |
| prime radical | C2×#121×D59 | C2 |
| hypercenter | #2639 | D59 |
| hypocenter | C59 | C2×#2639 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #2639 | |
3326 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3776 |
992 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 336000);