Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22⋊C4×Dic6 |
| Sylow | C3 ⋊ Q8×C22⋊C4 |
820 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)(12,14,15,19)(13,16,17,18);(2,3)(12,13,15,17)(14,18,19,16);(9,11);(4,5,6,7)(8,9)(10,11)90 conjugacy classes — view the full character table.
| maximal subgroup of | #10691626, #10691630, #10691654, … |
| maximal normal subgroup of | #10691626, #10691630, #10691654, … |
| maximal quotient of | C22⋊C4×C4⋊Dic3, C22⋊C4×Dic3⋊C4, Dic6×#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6029);