Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C59×#3407 ⋊ C2 |
| Sylow | C59 ⋊ #62624 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C24×D59 |
| commutator, socle | C2×C59 | C24×C8 |
| Fitting | C59×#3407 | C2 |
| prime radical | #16838238 | C4 |
| cosocle | C8×C59 | C25 |
| hypercenter | #3407 | D59 |
| hypocenter | C59 | #62624 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C8 ◁ #3407 | |
2038 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3776 |
Polycyclic presentation:
2^8,59|a^2=f,f^2=g,g^2=h,i^a=i^58,e^b=eh,d^c=dh,i^e=i^582108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 1076040);