Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of D112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C7×C16 ⋊ C2 |
| 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)(8,10,11,19,23,33,38,39,13,21,25,35,12,20,24,34)(9,14,27,31,26,30,22,32,16,28,15,18,17,29,37,36);(2,3)(4,5)(6,7)(8,9)(10,18)(11,22)(12,26)(13,16)(14,19)(15,24)(17,23)(20,36)(21,31)(25,37)(27,38)(28,35)(29,39)(30,34)(32,33)Polycyclic presentation:
2^6,7|b^2=cd,c^2=ef,e^2=f,b^a=bc,c^a=ce,d^a=df,e^a=ef,g^a=g^6118 conjugacy classes — view the full character table.
| maximal subgroup of | #11726821, #11726839, #11726880, … |
| maximal normal subgroup of | #11726821, #11726839, #11726880, … |
| maximal quotient of | #11725310, #11725311, #11725333, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 67);