Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#103 ⋊ C2 |
| Sylow | C7 ⋊ #419 |
150 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 55 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)(13,18)(14,20)(15,23)(17,24)(21,22)(25,27);(12,14,16,22)(13,17,18,25)(15,20,23,21)(19,27,26,24);(2,3)(4,5)(6,7)(12,13)(14,17)(15,19)(16,18)(20,27)(21,24)(22,25)(23,26)Polycyclic presentation:
2^6,7|b^2=f,c^2=d,e^2=f,c^a=cf,g^a=g^6,c^b=ce,e^b=ef,e^c=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89574, #11736235, #11736255, … |
| maximal normal subgroup of | C2×#89574, #11736235, #11736255, … |
| maximal quotient of | #11725985, #11725989, #11725993, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 336);