Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#4493 |
| Sylow | C3 ⋊ C2×#368 |
144 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 37 points:
(3,4,5)(6,8,9,17,11,20,22,19)(7,12,13,25,15,27,29,26)(10,23,21,18,24,34,36,35)(14,30,28,16,31,32,37,33);(4,5)(6,7,10,14,22,29,36,37,11,15,24,31,9,13,21,28)(8,16,18,25,17,32,34,27,20,33,35,26,19,30,23,12);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10710575, #10710577, #10710580, … |
| maximal normal subgroup of | #10710575, #10710577, #10710580, … |
| maximal quotient of | C2×#67469, C2×#67470, #10706770, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3258);