Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C7×Q8 ⋊ C2 |
| Sylow | C7 ⋊ #448 |
158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(12,13,15,17)(14,19,18,16);(9,11);(2,3)(4,5)(6,7)(8,9)(10,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^6,7|c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,d^c=df79 conjugacy classes — view the full character table.
| maximal subgroup of | #11727453, #11727454, #11727459, … |
| maximal normal subgroup of | #11727453, #11727454, #11727459, … |
| maximal quotient of | #11729310, #11729314, #11729383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 761);