Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2971 |
402 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 221 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)(4,6,7,10)(5,9,8,11)(12,15,16,17)(13,14,18,19);(2,3)(12,14,17,18,16,19,15,13);(5,8)(9,11)(13,18)(14,19);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13,17,14,16,18,15,19)Polycyclic presentation:
2^7,3|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=dg,h^a=h^2,c^b=cg,d^c=dg,h^c=h^290 conjugacy classes — view the full character table.
| maximal subgroup of | #10690987, #10690991, #10691001, … |
| maximal normal subgroup of | #10690987, #10690991, #10691001, … |
| maximal quotient of | #10793477, #10793628, Q8×#803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15095);