Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | D59×#2388 |
| Fitting | C59×#2388 ⋊ C2 |
| Sylow | C59 ⋊ C2×#2388 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D59 |
| commutator, socle, cosocle | C23×C59 | C25 |
| Frattini | C23 | C24×D59 |
| Fitting | C59×#2388 | C2 |
| hypercenter | #2388 | D59 |
| hypocenter | C59 | C2×#2388 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ #2388 | |
6238 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, 335760);