Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2045 |
296 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 71 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) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,3)(5,7)(8,10,11,19,12,18,20,23)(9,14,15,22,16,17,13,21);(1,2,3)(9,13)(10,18)(11,20)(14,22)(15,16)(17,21);(4,5)(6,7)(8,9)(10,17)(11,13)(12,16)(14,18)(15,20)(19,22)(21,23)Polycyclic presentation:
2^7,3|c^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,c^b=cf,d^b=dg,e^c=eg,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10707660, #10707665, #10707670, … |
| maximal normal subgroup of | #10707660, #10707665, #10707670, … |
| maximal quotient of | #10698750, #10698757, #10698806, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4618);