Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #380 |
234 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(8,9,10,11)(13,15)(17,19);(16,17,18,19);(2,3)(4,5)(6,7)(12,13)(14,15)Polycyclic presentation:
2^6,7|b^2=f,c^2=d,c^a=ce,g^a=g^6,c^b=cf88 conjugacy classes — view the full character table.
| maximal subgroup of | #11726567, #11726576, #11726577, … |
| maximal normal subgroup of | #11726567, #11726576, #11726577, … |
| maximal quotient of | #11727156, #11727164, (C2×D7)⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 521);