Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#124 ⋊ C2 |
| Sylow | C7 ⋊ #454 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6500 |
| commutator, cosocle | C2×C4×C7 | C23 |
| Frattini | C2×C4 | C22×D7 |
| Fitting | C7×#124 | C2 |
| socle | C2×C7 | #120 |
| hypercenter | #124 | D7 |
| hypocenter | C7 | #454 |
| LCS | G ▷ C2×C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #124 | |
146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(9,14)(11,20)(13,21)(15,16)(17,19)(22,23);(8,10,12,18)(9,13,16,23)(11,19,20,17)(14,22,15,21);(2,3)(4,5)(6,7)(8,9)(10,13)(11,14)(12,16)(15,20)(17,21)(18,23)(19,22)Polycyclic presentation:
2^6,7|b^2=f,d^2=f,c^a=cd,d^a=df,e^a=ef,g^a=g^6,c^b=ce,d^b=df,d^c=df58 conjugacy classes — view the full character table.
| maximal subgroup of | #11725266, #11725348, #11726914, … |
| maximal normal subgroup of | #11725266, #11725348, #11726914, … |
| maximal quotient of | #11727297, #11727316, #11727317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 596);