Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C3 ⋊ #1747 |
200 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 200 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) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(2,3)(4,7,8,18,9,19,20,31)(5,11,12,23,13,24,25,33)(6,15,16,28,17,29,30,35)(10,21,14,26,22,32,27,34);(1,2,3)(4,6)(5,10,13,22)(7,15)(8,16)(9,17)(11,21,24,32)(12,14,25,27)(18,28)(19,29)(20,30)(23,26,33,34)(31,35);(4,5)(6,14,17,27)(7,11)(8,12)(9,13)(10,16,22,30)(15,26,29,34)(18,23)(19,24)(20,25)(21,28,32,35)(31,33)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=d,d^2=g,b^a=bd,f^a=fg,e^b=eg,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10705720, #10705722, #10705727, … |
| maximal normal subgroup of | #10705720, #10705722, #10705727, … |
| maximal quotient of | #10685625, #10685627, #10685629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1273);