Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of D112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C7×C16 ⋊ C2 |
| Sylow | C7 ⋊ #357 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,4,6,7,5,3)(8,9,10,11)(12,13,18,24,15,19,22,25,16,20,26,27,21,23,14,17);(2,3)(4,5)(6,7)(13,17)(14,18)(15,21)(19,27)(20,25)(22,26)(23,24)Polycyclic presentation:
2^6,7|b^2=cde,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^6118 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D112, #11726812, #11726813, … |
| maximal normal subgroup of | C4×D112, #11726812, #11726813, … |
| maximal quotient of | #11725310, #11725332, #11725366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 66);