Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #497 |
124 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)(9,11)(13,18)(14,21)(15,23)(17,24)(19,20)(25,26);(8,9,10,11)(12,14)(13,17)(15,22)(16,21)(18,26)(19,24)(20,25)(23,27);(2,3)(4,5)(6,7)(9,11)(12,13,16,20)(14,17,21,25)(15,18,23,19)(22,26,27,24)Polycyclic presentation:
2^6,7|a^2=f,b^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,c^b=cef,d^c=df58 conjugacy classes — view the full character table.
| maximal subgroup of | #11725351, #11725355, #11726107, … |
| maximal normal subgroup of | #11725351, #11725355, #11726107, … |
| maximal quotient of | #11727304, #11727306, #11727315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 594);