Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | M16×Dic6 |
| Sylow | C3 ⋊ Q8×M16 |
388 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(4,6,7,11)(5,8,9,10);(2,3)(4,5,7,9)(6,10,11,8);(13,16)(17,19);(12,13,14,17,15,16,18,19)90 conjugacy classes — view the full character table.
| maximal subgroup of | #10689521, #10689525, #10689535, … |
| maximal normal subgroup of | #10689521, #10689525, #10689535, … |
| maximal quotient of | M16×C4⋊Dic3, M16×Dic3⋊C4, #10793836, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11085);