Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1572 |
150 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 150 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)(6,12)(9,15)(13,18)(16,19)(20,23,25,24)(21,27,28,33)(22,30,32,31)(26,29,34,35);(2,3)(4,6)(5,9)(7,13)(8,12)(10,16)(11,15)(14,18)(17,19)(20,22,24,31,25,32,23,30)(21,26,27,29,28,34,33,35);(4,5,7,10,8,11,14,17)(6,9,13,16,12,15,18,19)(20,21)(22,29)(23,27)(24,33)(25,28)(26,31)(30,34)(32,35)Polycyclic presentation:
2^7,3|a^2=e,b^2=d,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cg,h^b=h^278 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1572, C2×#70747, #10764258, … |
| maximal normal subgroup of | D3×#1572, C2×#70747, #10764258, … |
| maximal quotient of | #10684666, #10686395, #10686400, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3323);