Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68807 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C3×D8 ⋊ C2 |
| Sylow | C3 ⋊ #1999 |
496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(5,7)(9,11);(1,2,3)(8,9)(10,11)(13,16)(14,19)(17,18);(4,5)(6,7)(12,13)(14,16)(15,18)(17,19)Polycyclic presentation:
2^7,3|d^2=g,b^a=bd,c^a=ce,d^a=dg,c^b=cf,d^b=dg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10707282, #10707287, #10707292, … |
| maximal normal subgroup of | #10707282, #10707287, #10707292, … |
| maximal quotient of | #10695380, #10695387, #10695408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4619);