Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#100 ⋊ 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)(8,10,11,18,12,17,20,23)(9,13,14,16,15,21,19,22);(10,17)(11,20)(14,19)(16,22);(2,3)(4,5)(6,7)(8,9)(10,16)(11,19)(12,15)(13,18)(14,20)(17,22)(21,23)Polycyclic presentation:
2^6,7|c^2=d,d^2=f,c^a=cd,d^a=df,e^a=ef,g^a=g^6,c^b=ce,d^b=df,e^c=ef49 conjugacy classes — view the full character table.
| maximal subgroup of | #11726885, #11726886, #11726892, … |
| maximal normal subgroup of | #11726885, #11726886, #11726892, … |
| maximal quotient of | #11725862, #11725863, #11725864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 280);