Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1814 |
256 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 89 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:
(1,2,3)(4,7)(5,12)(6,16)(8,21)(9,24)(10,22)(11,25)(13,27)(14,28)(15,29)(17,31)(18,33)(19,32)(20,23)(26,35)(30,34);(2,3)(4,6,8,17,10,19,9,18)(5,11,13,15,14,26,23,30)(7,16,21,31,22,32,24,33)(12,25,27,29,28,35,20,34);(4,5)(6,15)(7,20,22,27)(8,23)(9,13)(10,14)(11,17)(12,21,28,24)(16,25,32,35)(18,26)(19,30)(29,31,34,33)Polycyclic presentation:
2^7,3|a^2=f,b^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^2,e^c=eg,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1814, C2×#70396, #10794851, … |
| maximal normal subgroup of | D3×#1814, C2×#70396, #10794851, … |
| maximal quotient of | #10688059, #10688064, #10688069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2972);