Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C7×Q16 ⋊ C2 |
| Sylow | C7 ⋊ #464 |
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 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)(9,11)(12,14,16,20)(13,17,19,26)(15,24,25,22)(18,27,23,21);(12,13,16,19)(14,21,20,27)(15,23,25,18)(17,24,26,22);(2,3)(4,5)(6,7)(8,9,10,11)(14,20)(17,26)(21,27)(22,24)Polycyclic presentation:
2^6,7|a^2=e,b^2=f,c^2=f,d^2=f,c^a=cef,g^a=g^6,c^b=cd,d^b=df,d^c=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11737145, #11737146, #11737148, … |
| maximal normal subgroup of | #11737145, #11737146, #11737148, … |
| maximal quotient of | #11727976, #11727984, #11727988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 719);