Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#510 ⋊ C2 |
| Sylow | C3 ⋊ #2212 |
154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 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)(8,20)(9,26)(10,22)(11,27)(13,28)(14,31)(15,30)(17,33)(18,34)(19,25)(21,24)(23,29)(32,35);(2,3)(4,6,8,17,10,18,24,9)(5,11,13,14,15,25,23,32)(7,16,20,33,22,34,21,26)(12,27,28,31,30,19,29,35);(2,3)(4,5)(6,14)(7,19)(8,23)(9,25)(10,15)(11,17)(12,16)(13,24)(18,32)(20,31)(21,35)(22,27)(26,28)(29,33)(30,34)Polycyclic presentation:
2^7,3|b^2=d,d^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,h^a=h^2,h^b=h^2,e^c=ef,f^c=fg39 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2212, C2×#71519, #10949577, … |
| maximal normal subgroup of | D3×#2212, C2×#71519, #10949577, … |
| maximal quotient of | #10709305, #10709312, #10709329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4095);