Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#107 ⋊ C2 |
| Sylow | C7 ⋊ C4×D8 |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(8,10,11,9)(13,16)(14,19)(17,18);(8,9,11,10)(12,13)(14,16)(15,18)(17,19);(2,3)(4,5)(6,7)(8,9,11,10)Polycyclic presentation:
2^6,7|a^2=e,b^2=e,c^2=e,d^2=f,g^a=g^6,c^b=cd,d^b=df,d^c=df70 conjugacy classes — view the full character table.
| maximal subgroup of | #11726928, #11726931, #11726956, … |
| maximal normal subgroup of | #11726928, #11726931, #11726956, … |
| maximal quotient of | #11726310, #11726313, #11726317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 406);