Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#4696 |
| Fitting | C2×C3×C4×C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×#495 |
592 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 181 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 — 4 generators on 25 points:
(3,4,5)(10,12,13,19,14,20,22,25)(11,16,17,18,15,23,21,24);(6,7,8,9)(11,15)(16,23)(17,21)(18,24);(1,2)(4,5)(7,9)(10,11)(12,18)(13,21)(14,15)(16,19)(17,22)(20,24)(23,25);(1,2)108 conjugacy classes — view the full character table.
| maximal subgroup of | #10694728, #10694730, #10694752, … |
| maximal normal subgroup of | #10694728, #10694730, #10694752, … |
| maximal quotient of | C2×#68058, C2×#68063, C2×#68059, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11042);