Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C7×#124 ⋊ C2 |
| Sylow | C7 ⋊ #495 |
130 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(14,22)(15,24)(17,25)(19,20)(21,26);(8,9,10,11)(12,14)(13,17)(15,23)(16,22)(18,26)(19,25)(20,21)(24,27);(2,3)(4,5)(6,7)(9,11)(12,13)(14,21)(15,18)(16,20)(17,22)(19,24)(23,25)(26,27)Polycyclic presentation:
2^6,7|b^2=ef,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,c^b=ce,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | #11737734, #11737741, #11737969, … |
| maximal normal subgroup of | #11737734, #11737741, #11737969, … |
| maximal quotient of | #11727303, #11727305, #11727312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 593);