Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C269 ⋊ #405 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=e,d^2=f,g^a=g^268,c^b=cf,g^b=g^2682720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46810639, #46810641, #46810684, … |
| maximal normal subgroup of | #46810639, #46810641, #46810684, … |
| maximal quotient of | M16×#14524130, #46809169, #46809172, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 507);