Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | D59×#3509 |
| Fitting | C59×#3509 ⋊ C2 |
| Sylow | C59 ⋊ C2×#3509 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D59 |
| commutator, socle, cosocle | C22×C59 | C26 |
| Fitting | C59×#3509 | C2 |
| prime radical | C2×#41×D59 | C22 |
| hypercenter | #3509 | D59 |
| hypocenter | C59 | C2×#3509 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #3509 | |
7022 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3776 |
1364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 1078002);