Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #69507 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2074 |
222 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3)(5,7)(8,10,11,14)(9,13,12,15)(17,22)(18,24)(19,27)(21,28)(25,26)(29,31);(2,3)(9,12)(13,15)(16,18,20,26)(17,21,22,29)(19,24,27,25)(23,31,30,28);(4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17)(18,21)(19,23)(20,22)(24,31)(25,28)(26,29)(27,30)Polycyclic presentation:
2^7,3|a^2=e,b^2=g,c^2=d,f^2=g,b^a=bd,c^a=ceg,c^b=cf,f^b=fg,h^b=h^2,f^c=fg60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2074, C2×#69560, #10823941, … |
| maximal normal subgroup of | D3×#2074, C2×#69560, #10823941, … |
| maximal quotient of | #10699932, #10699937, #10699949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2136);