Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#124 ⋊ C2 |
| Sylow | C7 ⋊ #455 |
152 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)(8,10,12,18)(9,13,15,22)(11,21,20,17)(14,23,19,16);(11,20)(13,22)(14,19)(17,21);(2,3)(4,5)(6,7)(8,9)(10,16)(11,19)(12,15)(13,17)(14,20)(18,23)(21,22)Polycyclic presentation:
2^6,7|c^2=f,d^2=f,c^a=cd,d^a=df,e^a=ef,g^a=g^6,c^b=ce,d^b=df,d^c=df58 conjugacy classes — view the full character table.
| maximal subgroup of | #11725267, #11725352, #11726907, … |
| maximal normal subgroup of | #11725267, #11725352, #11726907, … |
| maximal quotient of | #11727297, #11727316, #11727317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 595);