Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4887 |
| Fitting | C2×C3×#107 ⋊ C2 |
| Sylow | C3 ⋊ C2×#467 |
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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)(12,18)(14,21)(15,22)(19,20)(23,25);(10,12,14,20,13,19,21,18)(11,15,17,22,16,23,24,25);(1,2)(4,5)(7,9)(10,11)(12,15)(13,16)(14,17)(18,25)(19,23)(20,22)(21,24);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10712134, #10712139, #10712190, … |
| maximal normal subgroup of | #10712134, #10712139, #10712190, … |
| maximal quotient of | C2×#68577, C2×#68579, C2×#68581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11724);