Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#4508 |
| Fitting | C22×C3×C16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#350 |
224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 93 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)(6,8,9,18,10,19,22,32,11,20,23,33,24,34,36,37)(7,12,13,25,15,26,29,31,16,27,21,35,14,17,28,30);(4,5)(6,7)(8,17)(9,21)(10,15)(11,16)(12,19)(13,23)(14,24)(18,31)(20,26)(22,28)(25,37)(27,34)(29,36)(30,33)(32,35);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10710234, C4×#4508, #10710239, … |
| maximal normal subgroup of | #10710234, C4×#4508, #10710239, … |
| maximal quotient of | C2×#67523, #10704261, C2×#67525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3986);