Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#4880 |
| Fitting | C2×C3×#107 ⋊ C2 |
| Sylow | C3 ⋊ C2×#427 |
512 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 512 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)(6,7,8,9)(11,16)(12,18)(13,21)(15,22)(19,20)(23,25);(10,12,13,19,14,20,21,18)(11,15,17,22,16,23,24,25);(1,2)(4,5)(10,11)(12,15)(13,17)(14,16)(18,25)(19,22)(20,23)(21,24);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10710065, #10710068, #10710112, … |
| maximal normal subgroup of | #10710065, #10710068, #10710112, … |
| maximal quotient of | C2×#68567, C2×#68570, #10764199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11720);