Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C7 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D7 |
| commutator, socle | C2×C7 | C23×C4 |
| Fitting, prime radical | C2×C7×#41 | C2 |
| cosocle | C4×C7 | C24 |
| hypercenter | C2×#41 | D7 |
| hypocenter | C7 | #568 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
258 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,4,6,7,5,3)(9,14)(13,19)(15,21)(20,23);(10,16)(13,19)(17,22)(20,23);(8,10)(9,13)(11,17)(12,16)(14,19)(15,20)(18,22)(21,23);(2,3)(4,5)(6,7)(8,9,11,15,12,14,18,21)(10,13,17,20,16,19,22,23)Polycyclic presentation:
2^6,7|a^2=e,e^2=f,d^a=df,g^a=g^6,c^b=cf94 conjugacy classes — view the full character table.
| maximal subgroup of | #11727755, #11727756, #11727798, … |
| maximal normal subgroup of | #11727755, #11727756, #11727798, … |
| maximal quotient of | #11739647, #11739649, #11739654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1272);