Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C59×#2285 ⋊ C2 |
| Sylow | C59 ⋊ #36684 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D59 |
| commutator, socle, cosocle | C23×C59 | C25 |
| Frattini | C23 | C24×D59 |
| Fitting | C59×#2285 | C2 |
| hypercenter | #2285 | D59 |
| hypocenter | C59 | #36684 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ #2285 | |
2138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7552 |
Polycyclic presentation:
2^8,59|b^2=h,e^2=f,b^a=bf,c^a=cg,d^a=dh,i^a=i^58,c^b=ch,d^c=dfh,i^c=i^581676 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 376119);