Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22⋊C4×#67 |
| Fitting | C22×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(13,15);(2,3)(12,13)(14,15);(9,11);(4,5,6,7)(8,9)(10,11)90 conjugacy classes — view the full character table.
| maximal subgroup of | #10810507, #67×#99, #10811315, … |
| maximal normal subgroup of | #10810507, #67×#99, #10811315, … |
| maximal quotient of | C22⋊C4×(C2×D3)⋊C4, C22⋊C4×#217, C22⋊C4×Dic3⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14698);