Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #428 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(8,10,11,9)(12,13)(14,19)(15,17)(16,18);(13,17)(16,19);(2,3)(4,5)(6,7)(8,9,11,10)(13,16)(14,18)(17,19)Polycyclic presentation:
2^6,7|a^2=e,c^2=e,d^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=cf,d^c=df82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726487, #11726488, #11726489, … |
| maximal normal subgroup of | #11726487, #11726488, #11726489, … |
| maximal quotient of | #11727220, #11727221, #11727235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 529);