Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D7 |
| commutator, socle, prime radical, cosocle | C22×C7 | C24 |
| Fitting | C7×C4⋊Q8 | C2 |
| hypercenter | C4⋊Q8 | D7 |
| hypocenter | C7 | Q82 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
212 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,4,6,7,5,3)(8,10)(9,13)(11,15)(12,14)(16,18,19,23)(17,20,21,22);(8,10,11,15)(9,13,14,12)(16,17,19,21)(18,22,23,20);(8,10,11,15)(9,12,14,13);(2,3)(4,5)(6,7)(8,9,11,14)(10,13,15,12)Polycyclic presentation:
2^6,7|a^2=f,b^2=f,c^2=e,d^2=ef,b^a=bf,g^a=g^6,d^b=df,d^c=de67 conjugacy classes — view the full character table.
| maximal subgroup of | #11726258, #11726259, #11726261, … |
| maximal normal subgroup of | #11726258, #11726259, #11726261, … |
| maximal quotient of | #11731768, #11731776, #11731780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1175);