Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3165 |
380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(13,17)(16,19);(2,3)(12,13,14,16,15,17,18,19);(4,6,7,11)(5,8,9,10);(2,3)(4,5,7,9)(6,10,11,8)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=e,c^2=f,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,d^c=dg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10692695, #10692697, #10692731, … |
| maximal normal subgroup of | #10692695, #10692697, #10692731, … |
| maximal quotient of | #10795617, #10798578, #10799771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15917);