Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×#4552 |
| Sylow | C3 ⋊ C2×#341 |
392 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 25 points:
(3,4,5)(6,7)(8,9)(10,12,14,21,15,22,13,20)(11,16,17,19,18,24,23,25);(4,5)(7,9)(10,11,13,17,15,18,14,23)(12,19,20,24,22,25,21,16);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10682333, #10682335, #10682339, … |
| maximal normal subgroup of | #10682333, #10682335, #10682339, … |
| maximal quotient of | C2×#67654, #10684646, #10684653, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4552);