Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4964 |
| Sylow | C3 ⋊ C2×#428 |
536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(6,7,8,9)(11,15)(12,17)(14,16);(1,2)(11,14)(15,16);(4,5)(10,11,12,16,13,14,17,15);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10701265, #10701267, #10701286, … |
| maximal normal subgroup of | #10701265, #10701267, #10701286, … |
| maximal quotient of | C2×#70420, C2×#70492, #10764214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14710);