Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×C22⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ #452 |
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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)(12,15,16,23,17,24,14,21)(13,19,18,22,20,26,25,27);(8,9)(10,11)(12,14,17,16)(13,18,20,25)(15,21,24,23)(19,22,26,27);(2,3)(4,5)(6,7)(12,13)(14,18)(15,22)(16,25)(17,20)(19,23)(21,26)(24,27)Polycyclic presentation:
2^6,7|b^2=f,c^2=d,d^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=ce79 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89505, #11736055, #11736059, … |
| maximal normal subgroup of | C2×#89505, #11736055, #11736059, … |
| maximal quotient of | #11725863, #11725867, #11725886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 267);