Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#103 ⋊ C2 |
| Sylow | C7 ⋊ #467 |
114 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 41 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)(8,9)(10,11)(12,15,17,14)(13,18,20,22)(16,21,23,24)(19,26,27,25);(9,11)(12,14,16,21,17,15,23,24)(13,18,19,25,20,22,27,26);(2,3)(4,5)(6,7)(9,11)(12,13)(14,18)(15,22)(16,19)(17,20)(21,25)(23,27)(24,26)Polycyclic presentation:
2^6,7|b^2=d,c^2=f,d^2=f,e^2=f,c^a=cde,g^a=g^6,c^b=cef,d^c=df,e^c=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89585, #11736245, #11736251, … |
| maximal normal subgroup of | C2×#89585, #11736245, #11736251, … |
| maximal quotient of | #11726195, #11726201, #11726219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 347);