Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#5395 |
| Fitting | C2×C4×Q8 ⋊ D3 |
305 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 305 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) = 64 |
A minimal faithful permutation representation — 3 generators on 22 points:
(3,4,5,6)(7,10,17)(8,19,21,12,13,22)(9,15,18)(14,20);(4,6)(7,8)(9,12)(10,14)(11,13)(15,20)(16,19)(17,22)(18,21);(1,2)46 conjugacy classes — view the full character table.
| maximal subgroup of | #11711192, C4×#5395, #11712847, … |
| maximal normal subgroup of | #11711192, C4×#5395, #11712847, … |
| maximal quotient of | C2×#73023, C2×#73011, C2×#73024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17904);