Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #69507 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2041 |
402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(5,7)(8,10,11,9)(12,13)(14,18)(15,17)(16,19);(1,2,3)(8,9)(10,11)(13,18)(14,15)(17,19);(4,5)(6,7)(9,10)(13,17)(14,15)(18,19)Polycyclic presentation:
2^7,3|c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,e^b=eg,f^b=fg,e^c=eg,f^c=fg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10683887, #10683888, #10683894, … |
| maximal normal subgroup of | #10683887, #10683888, #10683894, … |
| maximal quotient of | #10698508, #10698513, #10698542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4338);