Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #2912 |
476 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 293 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 — 4 generators on 23 points:
(1,2,3)(10,16)(14,21)(17,22)(19,23);(8,10)(9,14)(11,17)(12,16)(13,19)(15,21)(18,22)(20,23);(8,9,11,13,12,15,18,20)(10,14,17,19,16,21,22,23);(2,3)(4,5,6,7)(9,13)(11,18)(14,19)(15,20)(17,22)(21,23)Polycyclic presentation:
2^7,3|a^2=f,b^2=e,e^2=g,b^a=be,e^a=eg,h^a=h^2,d^c=dg84 conjugacy classes — view the full character table.
| maximal subgroup of | #10711502, #10711506, #10711507, … |
| maximal normal subgroup of | #10711502, #10711506, #10711507, … |
| maximal quotient of | #10764176, #10764230, #10764314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16360);