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.
| Sylow | C7 ⋊ #367 |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,4,6,7,5,3)(12,13,18,24,23,27,14,17,16,20,21,26,15,19,22,25);(2,3)(4,5)(6,7)(8,9,10,11)(13,17)(14,21)(15,23)(18,22)(19,26)(20,25)(24,27)Polycyclic presentation:
2^6,7|a^2=c,b^2=de,d^2=e,e^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^6118 conjugacy classes — view the full character table.
| maximal subgroup of | #11725388, #11725407, #11725412, … |
| maximal normal subgroup of | #11725388, #11725407, #11725412, … |
| maximal quotient of | #11725307, #11725407, #11725612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 62);