Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#103 ⋊ C2 |
| Sylow | C7 ⋊ #416 |
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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)(12,15,16,14,17,23,25,24)(13,19,20,22,21,26,27,18);(12,14,17,24)(13,18,21,22)(15,25,23,16)(19,20,26,27);(2,3)(4,5)(6,7)(12,13)(14,22)(15,19)(16,20)(17,21)(18,24)(23,26)(25,27)Polycyclic presentation:
2^6,7|b^2=f,c^2=d,d^2=f,e^2=f,b^a=bf,g^a=g^6,c^b=ce,d^b=df,e^b=ef70 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89576, #11736235, #11736252, … |
| maximal normal subgroup of | C2×#89576, #11736235, #11736252, … |
| maximal quotient of | #11725983, #11725987, #11725991, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 338);