Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C7×Q16 ⋊ C2 |
| Sylow | C7 ⋊ #473 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,4,6,7,5,3)(8,11,14,27)(9,16,18,33)(10,19,22,36)(12,26,13,25)(15,29,31,38)(17,34,28,23)(20,24,21,35)(30,39,37,32);(8,10,13,21,14,22,12,20)(9,15,17,30,18,31,28,37)(11,24,26,36,27,35,25,19)(16,32,23,38,33,39,34,29);(2,3)(4,5)(6,7)(8,9)(10,15)(11,23)(12,28)(13,17)(14,18)(16,25)(19,32)(20,37)(21,30)(22,31)(24,38)(26,33)(27,34)(29,35)(36,39)Polycyclic presentation:
2^6,7|b^2=e,c^2=f,d^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=ce,d^c=df,e^c=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | #11727024, #11727025, #11729244, … |
| maximal normal subgroup of | #11727024, #11727025, #11729244, … |
| maximal quotient of | #11728017, #11728018, #11728019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 726);