Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
127 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)(5,7,9,16,10,17,8,15)(6,11,12,14,13,19,18,20);(2,3)(5,6,8,12,10,13,9,18)(7,14,15,19,17,20,16,11)Polycyclic presentation:
2^5,3,2^2|a^2=c,b^2=d,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=h,h^a=g,g^f=h,h^f=gh44 conjugacy classes — view the full character table.
| maximal subgroup of | #11711516, #11711518, #11711519, … |
| maximal normal subgroup of | #11711516, #11711518, #11711519, … |
| maximal quotient of | #11711066, #11711067, #11711074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5681);