Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#99 ⋊ C2 |
| Sylow | C7 ⋊ #458 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6445 |
| commutator, cosocle | C23×C7 | C23 |
| Frattini | C23 | C22×D7 |
| Fitting | C7×#99 | C2 |
| socle | C2×C7 | #120 |
| prime radical | #6548 | C2 |
| hypercenter | #99 | D7 |
| hypocenter | C7 | #458 |
| LCS | G ▷ C23×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #99 | |
160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(8,11,12,19)(9,14,15,22)(10,16)(13,20)(17,18)(21,23);(8,10)(9,13)(11,18)(12,17)(14,20)(15,21)(16,19)(22,23);(2,3)(4,5)(6,7)(8,9)(10,13)(11,14)(12,15)(16,23)(17,21)(18,20)(19,22)Polycyclic presentation:
2^6,7|c^2=df,c^a=cd,e^a=ef,g^a=g^6,c^b=ce,d^b=df,e^c=ef49 conjugacy classes — view the full character table.
| maximal subgroup of | #11726886, #11726887, #11726894, … |
| maximal normal subgroup of | #11726886, #11726887, #11726894, … |
| maximal quotient of | #11725864, #11725865, #11725866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 276);