Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1393 |
232 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 57 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) = 96 |
A minimal faithful permutation representation — 2 generators on 15 points:
(1,2,3)(4,5,6,7)(9,12,14,13);(2,3)(8,9)(10,13,15,12)(11,14)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,h^a=h^2,d^b=dfg,d^c=dg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10682694, #10682695, #10682697, … |
| maximal normal subgroup of | #10682694, #10682695, #10682697, … |
| maximal quotient of | #10682150, #10682188, #10682212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 217);