Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89261 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ H(3,ℤ/4) |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(8,10,11,19,13,18,12,20)(9,14,15,17,16,22,21,23);(2,3)(4,5)(6,7)(8,9)(10,17,18,23)(11,21)(12,15)(13,16)(14,20,22,19)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,d^2=f,e^2=f,b^a=be,d^a=df,g^a=g^6,c^b=cf82 conjugacy classes — view the full character table.
| maximal subgroup of | #11725340, #11725342, #11725584, … |
| maximal normal subgroup of | #11725340, #11725342, #11725584, … |
| maximal quotient of | #11725466, #11725472, #11725482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 114);