Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #1783 |
820 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(5,7);(9,12)(10,14);(2,3)(4,5)(6,7)(8,9,10,13,11,12,14,15)Polycyclic presentation:
2^7,3|a^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,f^b=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10682458, #10682459, #10682474, … |
| maximal normal subgroup of | #10682458, #10682459, #10682474, … |
| maximal quotient of | #10686514, #10686528, #10686538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4705);