Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#4802 |
| Fitting | C2×C3×#103 ⋊ C2 |
| Sylow | C3 ⋊ C2×#419 |
752 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 229 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)(12,18)(13,21)(15,22)(19,20)(23,25);(6,7)(8,9)(10,12,14,20)(11,15,16,23)(13,18,21,19)(17,25,24,22);(1,2)(4,5)(10,11)(12,15)(13,17)(14,16)(18,25)(19,22)(20,23)(21,24);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4802, #10792970, #10793004, … |
| maximal normal subgroup of | C4×#4802, #10792970, #10793004, … |
| maximal quotient of | C2×#68231, C2×#68239, #10761630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11364);