Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×#67⋊C4 |
| Fitting | C22×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C22×C4×D4 |
2528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 15 points:
(1,2)(3,4)(5,6,7)(8,9,10,11)(13,15);(1,2)(3,4)(12,13)(14,15);(6,7)(13,15);(3,4);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10686522, #10686526, #10700606, … |
| maximal normal subgroup of | #10686522, #10686526, #10700606, … |
| maximal quotient of | C22×#4666, C22×Dic3×C22⋊C4, C22×#4649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18258);