Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #17304 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D59 |
| commutator, socle, prime radical, cosocle | C24×C59 | C24 |
| Fitting | C59×#1441 | C2 |
| hypercenter | #1441 | D59 |
| hypocenter | C59 | #17304 |
| LCS | G ▷ C24×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ #1441 | |
970 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15104 |
Polycyclic presentation:
2^8,59|a^2=efg,b^2=efh,c^2=g,d^2=e,b^a=be,c^a=cf,d^a=dh,i^a=i^58,c^b=cg,d^b=def,d^c=de1322 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 135108);