Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#5386 |
267 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 267 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2)(3,4,8)(6,9,10)(11,13,14,18)(12,15,16,17);(4,5)(7,9)(8,10)(11,12,14,16)(13,17,18,15);(1,2)46 conjugacy classes — view the full character table.
| maximal subgroup of | #11711120, #11711182, #11711196, … |
| maximal normal subgroup of | #11711120, #11711182, #11711196, … |
| maximal quotient of | C2×C4⋊#859, C2×#73059, C4×#5386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17890);