Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C22×#123×C59 ⋊ C2 |
| Sylow | C59 ⋊ #36710 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D59 |
| commutator, socle, cosocle | C23×C59 | C25 |
| Fitting | C22×#123×C59 | C2 |
| hypercenter | C22×#123 | D59 |
| hypocenter | C59 | #36710 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C22×#123 | |
2910 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3776 |
Polycyclic presentation:
2^8,59|b^2=f,c^2=f,d^2=f,b^a=bf,c^a=cg,d^a=df,e^a=efh,i^a=i^58,c^b=ch,d^b=dfh1676 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 376411);