Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4967 |
| Fitting | C22×C3×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C2×#480 |
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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)(6,7)(8,13)(9,11)(10,12)(14,16,17,20)(15,19,18,21);(1,2)(14,15)(16,19)(17,18)(20,21);(4,5)(7,10)(8,12)(11,13)(15,18)(19,21);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10690335, #10690341, #10691639, … |
| maximal normal subgroup of | #10690335, #10690341, #10691639, … |
| maximal quotient of | C2×#71553, C2×#71555, C2×#71560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14713);