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 ⋊ #2312 |
672 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 672 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) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(9,13)(12,14);(10,15)(12,14)(17,21)(20,23);(8,10)(9,12)(11,15)(13,14)(16,18,19,22)(17,20,21,23);(2,3)(4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17)(18,20)(19,21)(22,23)Polycyclic presentation:
2^7,3|a^2=g,b^2=f,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 | #10688650, #10688696, #10688700, … |
| maximal normal subgroup of | #10688650, #10688696, #10688700, … |
| maximal quotient of | #10716428, #10716444, #10716524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14669);