Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#5389 |
219 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 219 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,2)(3,5,6,10)(4,7,8,9)(11,14,21)(12,23,25,16,17,26)(13,19,22)(18,24);(3,4,6,8)(5,9,10,7)(11,12,13,16)(14,18,19,24)(15,17,20,23)(21,26,22,25);(1,2)46 conjugacy classes — view the full character table.
| maximal subgroup of | #11711193, C4×#5389, #11712879, … |
| maximal normal subgroup of | #11711193, C4×#5389, #11712879, … |
| maximal quotient of | C2×#73064, C2×#73062, C2×#73059, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17893);