Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C7×C8 ⋊ C2 |
| Sylow | C7 ⋊ #443 |
106 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)(8,11,12,21,14,20,13,10)(9,16,17,23,18,15,22,19);(8,10,13,20,14,21,12,11)(9,15,17,19,18,16,22,23);(2,3)(4,5)(6,7)(8,9)(10,19)(11,16)(12,17)(13,22)(14,18)(15,20)(21,23)Polycyclic presentation:
2^6,7|b^2=e,c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^6124 conjugacy classes — view the full character table.
| maximal subgroup of | #11725247, #11725249, #11725374, … |
| maximal normal subgroup of | #11725247, #11725249, #11725374, … |
| maximal quotient of | C8×D56, #11725806, C8×#1132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 234);