Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×Q8×C239 ⋊ C2 |
| Sylow | C239 ⋊ #393 |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=d,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^2382402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483498, #44483503, #44483525, … |
| maximal normal subgroup of | #44483498, #44483503, #44483525, … |
| maximal quotient of | #44482790, #44482807, #44482819, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 460);