Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#117 ⋊ C2 |
| Sylow | C7 ⋊ C4×#41 |
310 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 155 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 — 4 generators on 19 points:
(1,2,4,6,7,5,3)(8,9,10,11)(14,18)(16,19);(12,14)(13,16)(15,18)(17,19);(12,13,15,17)(14,16,18,19);(2,3)(4,5)(6,7)(14,18)(16,19)Polycyclic presentation:
2^6,7|b^2=f,d^2=e,c^a=cf,g^a=g^6,d^c=df100 conjugacy classes — view the full character table.
| maximal subgroup of | #11726465, #11726482, #11726483, … |
| maximal normal subgroup of | #11726465, #11726482, #11726483, … |
| maximal quotient of | #11730827, #11730829, #11730830, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 975);