Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2376 |
512 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 213 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)(9,13)(12,15)(17,20)(21,23);(9,13)(10,14)(16,18,19,22)(17,21,20,23);(8,10)(9,12)(11,14)(13,15)(16,17)(18,21)(19,20)(22,23);(2,3)(4,5,6,7)(8,9)(10,12)(11,13)(14,15)(17,20)(18,22)Polycyclic presentation:
2^7,3|a^2=g,c^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^2,c^b=cef,d^b=de66 conjugacy classes — view the full character table.
| maximal subgroup of | #10711959, #10711963, #10712466, … |
| maximal normal subgroup of | #10711959, #10711963, #10712466, … |
| maximal quotient of | #10716809, #10716818, #10716822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15416);