Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#405 ⋊ C2 |
| Sylow | C3 ⋊ #2951 |
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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)(8,10,12,18)(9,14,16,17)(11,19,20,23)(13,21,15,22);(4,6,7,5)(10,18)(14,17)(19,23)(21,22);(2,3)(9,13)(11,20)(14,21)(15,16)(17,22)(19,23);(2,3)(4,5,7,6)(8,9)(10,17)(11,13)(12,16)(14,18)(15,20)(19,22)(21,23)Polycyclic presentation:
2^7,3|a^2=f,c^2=f,d^2=g,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^2,e^b=eg,h^b=h^2,d^c=dg84 conjugacy classes — view the full character table.
| maximal subgroup of | #10711848, #10711852, #10711855, … |
| maximal normal subgroup of | #10711848, #10711852, #10711855, … |
| maximal quotient of | #10764670, #10764898, #10765041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11138);