Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#106 ⋊ C2 |
| Sylow | C7 ⋊ #470 |
110 conjugacy classes of subgroups.
| 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)(16,23)(17,24)(20,25)(22,27);(12,14,16,21,15,22,23,27)(13,17,19,25,18,20,26,24);(2,3)(4,5)(6,7)(9,11)(12,13)(14,20)(15,18)(16,19)(17,22)(21,24)(23,26)(25,27)Polycyclic presentation:
2^6,7|b^2=e,c^2=df,e^2=f,b^a=bf,c^a=cd,g^a=g^6,c^b=cef,e^c=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | #11727007, #11727068, C2×#89640, … |
| maximal normal subgroup of | #11727007, #11727068, C2×#89640, … |
| maximal quotient of | #11726295, #11726297, #11726299, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 402);