Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C7 ⋊ #365 |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(8,10,11,16,14,19,13,9)(12,21,20,23,22,15,17,18);(2,3)(4,5)(6,7)(8,9,12,15,13,10,17,18,14,16,22,21,11,19,20,23)Polycyclic presentation:
2^6,7|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bde,c^a=cf,g^a=g^6,d^b=de,e^b=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | #11727008, #11727011, #11727018, … |
| maximal normal subgroup of | #11727008, #11727011, #11727018, … |
| maximal quotient of | #11725270, #11725536, C2×#89289, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 51);