Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #359 |
56 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)(9,15)(11,20)(12,25)(13,29)(14,22)(16,30)(17,33)(18,32)(19,24)(21,26)(23,37)(27,39)(28,31)(34,35)(36,38);(2,3)(4,5)(6,7)(8,9,11,16,14,18,13,28)(10,19,20,35,22,36,29,33)(12,24,23,34,27,38,26,17)(15,25,30,37,32,39,31,21)Polycyclic presentation:
2^6,7|a^2=c,c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^6,d^b=de,e^b=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#359, #11726995, #11728675, … |
| maximal normal subgroup of | D7×#359, #11726995, #11728675, … |
| maximal quotient of | #11725530, #11725569, #11725571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 124);