Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#939 |
| Fitting | C2×C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ C4×#121 |
824 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(9,11)(13,15);(12,13)(14,15);(2,3)(8,9)(10,11)(13,15);(4,5,6,7)96 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#939, #10801212, #10801222, … |
| maximal normal subgroup of | C8×#939, #10801212, #10801222, … |
| maximal quotient of | C4×#5220, C4×#4958, C4×#4945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14896);