Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#5391 |
235 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 235 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) = 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)(11,13,20)(12,16,24)(15,21,22)(18,25,26);(3,4,6,8)(5,9,10,7)(11,12,15,18)(13,17,21,23)(14,16,19,25)(20,26,22,24);(1,2)46 conjugacy classes — view the full character table.
| maximal subgroup of | #11711118, #11711180, #11711195, … |
| maximal normal subgroup of | #11711118, #11711180, #11711195, … |
| maximal quotient of | C2×C4⋊#859, C2×#73062, C4×#5391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17897);