Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #451 |
148 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,7,5,3)(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20);(9,11);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21)Polycyclic presentation:
2^6,7|a^2=f,c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,d^c=df79 conjugacy classes — view the full character table.
| maximal subgroup of | #11727454, #11727455, #11727459, … |
| maximal normal subgroup of | #11727454, #11727455, #11727459, … |
| maximal quotient of | #11729309, #11729313, #11729382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 762);