Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ C4×#101 |
296 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 107 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 — 3 generators on 23 points:
(2,3)(4,6,7,5);(1,2,3)(8,10,12,18,11,17,19,23)(9,13,15,21,14,16,20,22);(4,5,7,6)(8,9,11,14)(10,16,17,13)(12,20,19,15)(18,21,23,22)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=eg,f^2=g,b^a=bd,f^a=fg,d^b=dg,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10705553, #10705555, #10705563, … |
| maximal normal subgroup of | #10705553, #10705555, #10705563, … |
| maximal quotient of | #10685692, #10685700, #10685704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1549);