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 ⋊ #2095 |
254 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 91 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) = 384 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(5,7)(16,18,20,17)(19,21,22,23);(2,3)(4,5)(6,7)(8,10,11,15)(9,12,13,14)(16,17)(18,20)(19,23)(21,22);(2,3)(8,9,11,13)(10,14,15,12)(16,17,19,21,20,18,22,23)Polycyclic presentation:
2^7,3|a^2=d,b^2=deg,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ceg,h^a=h^2,c^b=cf,d^b=dg,e^b=eg,h^b=h^2,d^c=dg,e^c=eg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10684448, #10684449, #10684486, … |
| maximal normal subgroup of | #10684448, #10684449, #10684486, … |
| maximal quotient of | #10700176, #10700209, #10700242, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2166);