Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1855 |
278 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 278 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)(5,7);(2,3)(8,10,12,18,13,19,11,21)(9,14,15,22,16,23,20,17);(4,5)(6,7)(8,9,12,15,13,16,11,20)(10,17,18,14,19,22,21,23)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,h^b=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10689197, #10689198, #10689202, … |
| maximal normal subgroup of | #10689197, #10689198, #10689202, … |
| maximal quotient of | #10689014, #10689019, #10689024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2560);