Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #431 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(17,21)(20,23);(16,18,19,22)(17,20,21,23);(2,3)(4,5)(6,7)(8,9,10,12,11,13,14,15)(16,17)(18,20)(19,21)(22,23)Polycyclic presentation:
2^6,7|a^2=d,b^2=e,d^2=f,c^a=ce,g^a=g^6136 conjugacy classes — view the full character table.
| maximal subgroup of | #11725417, #11725420, #11725426, … |
| maximal normal subgroup of | #11725417, #11725420, #11725426, … |
| maximal quotient of | #11727142, C4×C4⋊(C7⋊C8), #11727146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 459);