Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2554 |
560 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=eg,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^16358 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#2554, C2×#14533838, #17204508, … |
| maximal normal subgroup of | D17×#2554, C2×#14533838, #17204508, … |
| maximal quotient of | #16956622, #16956781, #16957562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 9564);