Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#102 ⋊ 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)(8,9,10,11)(13,18)(14,21)(16,24)(17,25)(20,27)(22,23);(12,14)(13,17)(15,22)(16,21)(18,20)(19,27)(23,24)(25,26);(2,3)(4,5)(6,7)(9,11)(12,13)(14,20)(15,18)(16,19)(17,22)(21,25)(23,27)(24,26)Polycyclic presentation:
2^6,7|c^2=df,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 | C2×#89555, #11736192, #11736204, … |
| maximal normal subgroup of | C2×#89555, #11736192, #11736204, … |
| maximal quotient of | #11725956, #11725957, #11725958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 317);