Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #1890 |
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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 — 3 generators on 23 points:
(1,2,3)(8,11)(9,14)(10,16)(12,19)(13,20)(15,18)(17,22)(21,23);(4,6,7,5)(8,10,12,17)(9,13,15,21)(11,16,19,22)(14,20,18,23);(2,3)(4,5,7,6)(8,9)(10,13)(11,18,19,14)(12,15)(16,20,22,23)(17,21)Polycyclic presentation:
2^7,3|a^2=f,b^2=dfg,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,e^b=eg,d^c=dg,f^c=fg66 conjugacy classes — view the full character table.
| maximal subgroup of | #10710954, #10710956, #10710991, … |
| maximal normal subgroup of | #10710954, #10710956, #10710991, … |
| maximal quotient of | #10689877, #10689887, #10690166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4231);