Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#837 |
| Sylow | C3 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(8,10)(9,12)(11,14)(13,15);(2,3)(8,9,11,13,12,10,15,14);(4,5,6,7)96 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#837, #10685898, #10685900, … |
| maximal normal subgroup of | C8×#837, #10685898, #10685900, … |
| maximal quotient of | C4×D4⋊(C3⋊C8), C4×#4535, #10685799, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4218);