Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×C8×Dic6 |
| Sylow | C3 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,8,9,13)(7,10,11,12);(1,2)(4,5)(6,7,9,11)(8,12,13,10);(14,15,16,18,17,19,20,21);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#824, #10685761, C8×#816, … |
| maximal normal subgroup of | C8×#824, #10685761, C8×#816, … |
| maximal quotient of | C2×C8×C4⋊Dic3, C2×C8×Dic3⋊C4, C4×C8×Dic6, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11019);