Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2060 |
246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 73 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) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,7,8,6)(5,9,10,11)(13,16)(14,19)(17,18);(4,6,8,7)(5,9,10,11)(14,19)(16,17);(2,3)(4,5,8,10)(6,11,7,9)(12,13)(14,16)(15,18)(17,19)Polycyclic presentation:
2^7,3|a^2=d,b^2=d,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,e^b=eg,e^c=eg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10682816, #10682818, #10708097, … |
| maximal normal subgroup of | #10682816, #10682818, #10708097, … |
| maximal quotient of | #10699590, #10699605, #10699617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2149);