Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4890 |
| Fitting | C2×C3×#107 ⋊ C2 |
| Sylow | C3 ⋊ C2×#474 |
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(7,11)(10,13)(14,15,19,21,17,20,16,18);(1,2)(6,8,9,12)(7,10,11,13)(15,18)(16,19)(20,21);(4,5)(6,7)(8,10)(9,11)(12,13)(15,18)(16,19)(20,21);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4890, #10802748, #10802821, … |
| maximal normal subgroup of | C4×#4890, #10802748, #10802821, … |
| maximal quotient of | C2×#68892, C2×#70638, C2×#68894, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11736);