Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #410 |
158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,11)(9,14)(10,16)(12,19)(13,20)(15,18)(17,23)(21,22);(8,10,12,17)(9,13,15,21)(11,16,19,23)(14,20,18,22);(2,3)(4,5)(6,7)(8,9)(10,13)(11,18,19,14)(12,15)(16,22,23,20)(17,21)Polycyclic presentation:
2^6,7|a^2=d,b^2=f,c^a=ce,e^a=ef,g^a=g^6,d^c=df82 conjugacy classes — view the full character table.
| maximal subgroup of | #11725497, #11725498, #11725502, … |
| maximal normal subgroup of | #11725497, #11725498, #11725502, … |
| maximal quotient of | #11729325, #11729326, #11729346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 774);