Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D4×#226 |
275 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 20 points:
(5,10,14,17,9,19,16,11)(6,15,18,8,12,7,20,13);(2,4)(7,13,16)(8,14,15)(10,17,20)(11,18,19);(1,2)(3,4)40 conjugacy classes — view the full character table.
| maximal subgroup of | #11712272, #11712273, #11712280, … |
| maximal normal subgroup of | #11712272, #11712273, #11712280, … |
| maximal quotient of | #11712312, #11712313, #11712316, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17966);