Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#4562 |
| Sylow | C3 ⋊ C2×#357 |
272 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 109 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)(10,11)(12,19)(13,22)(14,17)(15,18)(16,20)(21,24)(23,25);(4,5)(6,7,8,9)(11,15)(12,18)(13,20)(16,24)(17,23)(19,22)(21,25);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4562, Dic3×#357, #10710401, … |
| maximal normal subgroup of | C4×#4562, Dic3×#357, #10710401, … |
| maximal quotient of | C2×#67763, #10705162, #10705214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4608);