Finite Group DatabasebetaFinite Group Databasebeta| order | 2272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^5,71|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^b=f^70361 conjugacy classes — view the full character table.
| maximal subgroup of | #17986177, #17986178, #17986182, … |
| maximal normal subgroup of | #17986177, #17986178, #17986182, … |
| maximal quotient of | #17986000, #17986007, #17986042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2272, 176);