Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #2313 |
512 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 229 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)(17,20)(21,23);(9,13)(12,15)(16,18,19,22)(17,21,20,23);(8,10,11,14)(9,12,13,15)(17,20)(18,22);(2,3)(4,5,6,7)(8,9)(10,12)(11,13)(14,15)(16,17)(18,21)(19,20)(22,23)Polycyclic presentation:
2^7,3|a^2=g,b^2=f,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^2,c^b=ce84 conjugacy classes — view the full character table.
| maximal subgroup of | #10688653, #10688713, #10688717, … |
| maximal normal subgroup of | #10688653, #10688713, #10688717, … |
| maximal quotient of | #10716433, #10716444, #10716513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14731);