Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #340 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(12,13,14,15)(16,17,18,20,19,21,22,23);(2,3)(4,5)(6,7)(8,9,10,11)(17,20)(18,22)(21,23)Polycyclic presentation:
2^6,7|a^2=c,b^2=de,d^2=f,b^a=bd,d^a=df,g^a=g^6124 conjugacy classes — view the full character table.
| maximal subgroup of | #11725332, #11725334, #11725580, … |
| maximal normal subgroup of | #11725332, #11725334, #11725580, … |
| maximal quotient of | #11725460, #11725461, #11725481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 108);