Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C7×SD16 ⋊ C2 |
| Sylow | C7 ⋊ #452 |
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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)(12,14,16,21)(13,18,17,24)(15,23,22,20)(19,26,25,27);(13,17)(14,20)(15,22)(18,26)(21,23)(24,27);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,18)(15,19)(16,17)(20,27)(21,24)(22,25)(23,26)Polycyclic presentation:
2^6,7|c^2=f,e^2=f,b^a=bf,c^a=cd,g^a=g^6,c^b=ce,e^b=ef,e^c=ef61 conjugacy classes — view the full character table.
| maximal subgroup of | #11737097, #11737100, #11737102, … |
| maximal normal subgroup of | #11737097, #11737100, #11737102, … |
| maximal quotient of | #11727921, #11727953, #11727960, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 707);