Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2214 |
150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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)(5,13)(6,18)(8,22)(9,24)(10,25)(11,23)(12,21)(14,29)(15,31)(16,32)(17,30)(19,33)(20,28)(26,35)(27,34);(4,6,10,19,11,20,8,9)(5,12,16,26,17,27,14,15)(7,18,25,33,23,28,22,24)(13,21,32,35,30,34,29,31);(2,3)(4,5,11,17)(6,15,20,26)(7,21,23,34)(8,16,10,14)(9,12,19,27)(13,28,30,18)(22,35,25,31)(24,32,33,29)Polycyclic presentation:
2^7,3|a^2=g,b^2=dg,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,e^c=ef,f^c=fg51 conjugacy classes — view the full character table.
| maximal subgroup of | #10708590, #10708592, #10708595, … |
| maximal normal subgroup of | #10708590, #10708592, #10708595, … |
| maximal quotient of | #10709345, #10709352, #10709369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3503);