Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C7×2−1+4 ⋊ C2 |
| Sylow | C7 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D7 |
| commutator, socle, cosocle | C2×C7 | C25 |
| Fitting | C7×2−1+4 | C2 |
| hypercenter | 2−1+4 | D7 |
| hypocenter | C7 | #585 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 5 generators on 23 points:
(1,2,4,6,7,5,3)(8,11,12,18)(9,15,14,22)(10,16,17,19)(13,21,20,23);(9,14)(13,20)(15,22)(21,23);(8,10,12,17)(9,13,14,20)(11,19,18,16)(15,23,22,21);(8,9)(10,13)(11,15)(12,14)(16,21)(17,20)(18,22)(19,23);(2,3)(4,5)(6,7)(11,18)(15,22)(16,19)(21,23)Polycyclic presentation:
2^6,7|c^2=f,e^2=f,e^a=ef,g^a=g^6,d^b=df,e^c=ef85 conjugacy classes — view the full character table.
| maximal subgroup of | #11737729, #11737731, #11737743, … |
| maximal normal subgroup of | #11737729, #11737731, #11737743, … |
| maximal quotient of | #11742940, #11742941, #11742942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1382);