Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4836 |
| Fitting | C2×C3×C4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×#435 |
564 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,5)(7,9)(10,12,13,16,14,17,11,15);(1,2)(6,7,8,9)(10,11,14,13)(12,16,17,15);(4,5)(7,9);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10704418, #10793507, #10793512, … |
| maximal normal subgroup of | #10704418, #10793507, #10793512, … |
| maximal quotient of | C2×#68559, C2×#68520, C2×#68519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11578);