Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C22×C42 ⋊ D3 |
351 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 351 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,3,4)(5,6,8)(10,14)(13,16);(9,11,12,15)(10,13,14,16);(6,7)(9,10)(11,13)(12,14)(15,16)Polycyclic presentation:
2^5,3,2^2|b^2=e,c^2=d,c^a=ce,f^a=f^2,g^a=h,h^a=g,g^f=h,h^f=gh56 conjugacy classes — view the full character table.
| maximal subgroup of | #11712569, #11712572, #11712771, … |
| maximal normal subgroup of | #11712569, #11712572, #11712771, … |
| maximal quotient of | #11711683, C4×(C2×S4)⋊C4, C4×SL(2,ℤ/4)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17863);