Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C239 ⋊ #349 |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3824 |
Polycyclic presentation:
2^6,239|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^238,d^b=df2402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44482483, #44482484, #44482485, … |
| maximal normal subgroup of | #44482483, #44482484, #44482485, … |
| maximal quotient of | #44482472, #44482488, #44482506, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 331);