Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1470 |
204 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(4,7,8,15)(5,10,11,17)(6,13,14,19)(9,16,12,18)(22,28)(25,31)(29,34)(32,35);(2,3)(4,6,8,14)(5,9,11,12)(7,13,15,19)(10,16,17,18)(20,22)(21,25)(23,29)(24,28)(26,32)(27,31)(30,34)(33,35);(2,3)(4,5)(6,12,14,9)(7,10)(8,11)(13,18,19,16)(15,17)(20,21,23,26,24,27,30,33)(22,25,29,32,28,31,34,35)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^2,c^b=cg,e^b=ef,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10687442, #10687444, #10687452, … |
| maximal normal subgroup of | #10687442, #10687444, #10687452, … |
| maximal quotient of | #10683535, #10683548, #10683561, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3407);