Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C239 ⋊ #347 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3824 |
Polycyclic presentation:
2^6,239|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,g^a=g^238,c^b=cf2402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44482580, #44482581, #44482582, … |
| maximal normal subgroup of | #44482580, #44482581, #44482582, … |
| maximal quotient of | #44482469, #44482628, C2×#29504550 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 327);