Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×C4⋊C8 ⋊ 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)(12,14,15,22,16,21,24,27)(13,18,19,20,17,25,23,26);(8,9,10,11)(13,17)(14,21)(19,23)(22,27);(2,3)(4,5)(6,7)(9,11)(12,13)(14,20)(15,23)(16,17)(18,22)(19,24)(21,26)(25,27)Polycyclic presentation:
2^6,7|b^2=ef,c^2=d,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,c^b=ce79 conjugacy classes — view the full character table.
| maximal subgroup of | #11736466, #11736474, #11736475, … |
| maximal normal subgroup of | #11736466, #11736474, #11736475, … |
| maximal quotient of | #11726302, #11726303, #11726308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 379);