Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#123 ⋊ C4 |
| Sylow | C17 ⋊ #2374 |
552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=g,c^2=ef,d^2=ef,b^a=be,c^a=cf,h^a=h^4,d^b=de,h^b=h^13,h^g=h^16106 conjugacy classes — view the full character table.
| maximal subgroup of | #17961765, #17961925, C2×#14545322, … |
| maximal normal subgroup of | #17961765, #17961925, C2×#14545322, … |
| maximal quotient of | #17963040, #17963059, #17963065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21048);