Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#5425 |
319 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 319 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) = 22 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 22 points:
(3,4)(5,6)(7,15,20,8,10,22,12,13,18,9,19,21)(11,16,17,14);(4,6)(7,8,12,9)(10,14,19,16)(11,13,17,15)(18,22,20,21);(1,2)46 conjugacy classes — view the full character table.
| maximal subgroup of | #11711190, C4×#5425, #11712812, … |
| maximal normal subgroup of | #11711190, C4×#5425, #11712812, … |
| maximal quotient of | C2×#73093, C2×#73094, C2×#73090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18092);