Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #362 |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2,4,6,7,5,3)(8,10,13,22)(9,14,18,31)(11,23,25,20)(12,27,28,37)(15,30,17,29)(16,33,34,35)(19,26,36,32)(21,24,38,39);(2,3)(4,5)(6,7)(8,9,11,15,13,18,25,17)(10,19,20,33,22,36,23,35)(12,26,24,16,28,32,39,34)(14,27,29,21,31,37,30,38)Polycyclic presentation:
2^6,7|a^2=c,b^2=f,c^2=f,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^6,c^b=cf,d^b=def,e^b=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#362, #11727020, #11727021, … |
| maximal normal subgroup of | D7×#362, #11727020, #11727021, … |
| maximal quotient of | #11725529, #11725570, #11725583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 122);