Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5033 |
| 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)(15,18)(17,20)(19,21);(1,2)(16,20)(18,21);(4,5)(7,10)(8,12)(11,13)(14,15,17,19)(16,18,20,21);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10690336, #10690338, #10691638, … |
| maximal normal subgroup of | #10690336, #10690338, #10691638, … |
| maximal quotient of | C2×#69501, C2×#69504, C2×#71677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15189);