Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#5121 |
| Sylow | C3 ⋊ C2×#428 |
536 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(10,11,12,14,13,15,16,17);(1,2)(11,15)(14,17);(4,5)(6,7,8,9)(11,14)(12,16)(15,17);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10701269, #10701271, #10701290, … |
| maximal normal subgroup of | #10701269, #10701271, #10701290, … |
| maximal quotient of | C2×#69850, C2×#69851, #10764216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16327);