Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22×C16 ⋊ D3 |
95 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,4)(5,6,11,17,16,20,7,10,9,13,14,19,8,12,15,18);(2,3)(6,10)(7,14)(8,16)(11,15)(12,19)(13,18)(17,20)Polycyclic presentation:
2^5,3,2^2|b^2=cd,c^2=d,d^2=e,b^a=bc,c^a=cde,d^a=de,f^a=f^2,g^a=h,h^a=g,g^f=h,h^f=gh38 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73036, #11714191, #11714192, … |
| maximal normal subgroup of | C2×#73036, #11714191, #11714192, … |
| maximal quotient of | #11711472, #11711475, #11711477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5612);