Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C269 ⋊ C2×#97 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=e,d^2=f,b^a=bf,g^a=g^187,g^c=g^268,g^d=g^2681112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46825710, #46825762, #46825778 |
| maximal normal subgroup of | #46825710, #46825762, #46825778 |
| maximal quotient of | #46826081, #46826093, #46826099 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1508);