Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68629 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#336 ⋊ C2 |
| Sylow | C3 ⋊ #2092 |
274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(5,7)(17,21)(18,23)(20,22);(2,3)(4,5)(6,7)(8,10,11,15)(9,12,13,14)(17,20)(18,23)(21,22);(8,9,11,13)(10,14,15,12)(16,17,18,21,19,22,23,20)Polycyclic presentation:
2^7,3|a^2=d,b^2=deg,d^2=g,e^2=g,b^a=bd,c^a=ceg,c^b=cf,d^b=dg,e^b=eg,h^b=h^2,d^c=dg,e^c=eg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2092, C2×#68680, #10824985, … |
| maximal normal subgroup of | D3×#2092, C2×#68680, #10824985, … |
| maximal quotient of | #10700157, #10700191, #10700225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1256);