Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4487 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#4487 |
| Sylow | C3 ⋊ C2×#365 |
152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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) = 96 |
A minimal faithful permutation representation — 3 generators on 21 points:
(3,4,5)(7,11,12,13)(8,15)(9,17)(14,20,18,19)(16,21);(4,5)(6,7,8,13,9,14,15,20,10,12,16,11,17,18,21,19);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10710570, C4×#4487, #10710608, … |
| maximal normal subgroup of | #10710570, C4×#4487, #10710608, … |
| maximal quotient of | C2×#67464, #10706744, #10706818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3126);