Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #452 |
152 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 47 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)(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21);(12,14)(13,18)(15,22)(16,25)(17,23)(19,26)(20,27)(21,24);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,17,20)(14,21,23,26)(15,19,16,24)(18,25,27,22)Polycyclic presentation:
2^6,7|a^2=f,c^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^6,e^b=ef79 conjugacy classes — view the full character table.
| maximal subgroup of | #11736290, #11736292, #11736294, … |
| maximal normal subgroup of | #11736290, #11736292, #11736294, … |
| maximal quotient of | #11729330, #11729339, #11729360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 773);