Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2373 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=g,c^2=e,d^2=ef,b^a=be,c^a=cf,d^b=de,h^b=h^16370 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#2373, C2×#14531900, #17194026, … |
| maximal normal subgroup of | D17×#2373, C2×#14531900, #17194026, … |
| maximal quotient of | #16955781, #16955844, #16955855, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7626);