Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1316 |
294 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 41 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) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(13,16)(17,18);(2,3)(4,5,6,8,7,9,10,11)(12,13)(14,18,19,16)(15,17)Polycyclic presentation:
2^7,3|a^2=d,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,d^b=de,d^c=dg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10682533, #10682534, #10682559, … |
| maximal normal subgroup of | #10682533, #10682534, #10682559, … |
| maximal quotient of | #10681806, #10681814, #10681933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 198);