Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#5002 |
| Fitting | C2×C3×#117 ⋊ C2 |
| Sylow | C3 ⋊ C2×#416 |
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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)(6,8,9,7)(11,16)(13,21)(15,22)(17,18)(19,25)(23,24);(1,2)(10,12,14,20)(11,15,18,24)(13,19,21,25)(16,22,17,23);(4,5)(6,7)(8,9)(10,11)(12,15)(13,16)(14,18)(17,21)(19,22)(20,24)(23,25);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10700689, #10700691, #10700710, … |
| maximal normal subgroup of | #10700689, #10700691, #10700710, … |
| maximal quotient of | C2×#70754, C2×#70798, #10761597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14787);