Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #489 |
100 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)(9,13)(10,14)(16,17)(18,22)(19,20)(21,23);(8,10,11,14)(9,12,13,15)(17,20)(21,22);(2,3)(4,5)(6,7)(8,9)(10,12)(11,13)(14,15)(16,17,18,21,19,20,23,22)Polycyclic presentation:
2^6,7|a^2=e,b^2=d,e^2=f,b^a=bf,c^a=cde,g^a=g^6,c^b=cdf,e^c=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | #11726106, #11726111, #11726112, … |
| maximal normal subgroup of | #11726106, #11726111, #11726112, … |
| maximal quotient of | #11727296, #11727302, #11727309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 589);