Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #559 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D7 |
| commutator, socle, cosocle | C22×C7 | C24 |
| Fitting, prime radical | C7×#127 | C2 |
| hypercenter | #127 | D7 |
| hypocenter | C7 | #559 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #127 | |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,4,6,7,5,3)(9,13)(12,15)(16,18,19,23)(17,20,21,22);(10,14)(12,15)(18,23)(20,22);(8,10)(9,12)(11,14)(13,15)(18,23)(20,22);(2,3)(4,5)(6,7)(8,9)(10,12)(11,13)(14,15)(16,17,19,21)(18,22,23,20)Polycyclic presentation:
2^6,7|a^2=f,d^2=f,d^a=def,g^a=g^6,c^b=ce,d^b=df,d^c=df67 conjugacy classes — view the full character table.
| maximal subgroup of | #11726156, #11726158, #11726160, … |
| maximal normal subgroup of | #11726156, #11726158, #11726160, … |
| maximal quotient of | #11731770, #11731777, #11731786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1166);