Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C7×Q16 ⋊ C2 |
| Sylow | C7 ⋊ #497 |
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 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)(12,14,16,22)(13,18,19,27)(15,24,23,21)(17,25,26,20);(12,13,15,17,16,19,23,26)(14,20,21,27,22,25,24,18);(2,3)(4,5)(6,7)(8,9)(10,11)(13,17)(15,23)(18,25)(19,26)(20,27)(21,24)Polycyclic presentation:
2^6,7|b^2=e,c^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^6,c^b=ce,e^c=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | #11737158, #11737159, #11737171, … |
| maximal normal subgroup of | #11737158, #11737159, #11737171, … |
| maximal quotient of | #11727981, #11727982, #11728004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 724);