Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C7×Q8 ⋊ C2 |
| Sylow | C7 ⋊ #464 |
112 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 112 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)(12,14,16,22)(13,18,17,26)(15,24,25,21)(19,27,23,20);(8,9,10,11)(13,17)(18,26)(19,23)(20,27);(2,3)(4,5)(6,7)(9,11)(12,13)(14,20)(15,23)(16,17)(18,21)(19,25)(22,27)(24,26)Polycyclic presentation:
2^6,7|b^2=ef,c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,d^c=df79 conjugacy classes — view the full character table.
| maximal subgroup of | #11737069, #11737072, #11737084, … |
| maximal normal subgroup of | #11737069, #11737072, #11737084, … |
| maximal quotient of | #11727216, #11727218, #11727222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 562);