Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4867 |
| Fitting | C2×C3×#106 ⋊ C2 |
| Sylow | C3 ⋊ C2×#470 |
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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)(6,7,8,9)(11,16)(12,19)(14,21)(15,22)(18,23)(20,25);(10,12,14,19,13,20,21,25)(11,15,17,23,16,18,24,22);(1,2)(4,5)(7,9)(10,11)(12,18)(13,16)(14,17)(15,20)(19,22)(21,24)(23,25);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10712175, #10712226, #10713962, … |
| maximal normal subgroup of | #10712175, #10712226, #10713962, … |
| maximal quotient of | C2×#68541, C2×#68543, C2×#68545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11695);