Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
257 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 257 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 36 points:
(2,4)(5,32,20,18,21,33,10,16,23,7,8,31)(6,29,27,15,22,36,14,25,28,11,12,35)(9,17,24,34)(13,26,19,30);(1,2,3,4);(5,6,10,14)(7,15,18,11)(8,19,21,13)(9,22,24,12)(16,26,32,30)(17,25,34,29)(20,28,23,27)(31,35,33,36)Polycyclic presentation:
2^4,3,2^3|a^2=h,b^2=d,c^2=h,f^2=h,g^2=h,c^a=ch,e^a=e^2,f^a=gh,g^a=fh,c^b=cd,f^e=g,g^e=fgh,g^f=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | #11712273, #11712275, #11712308, … |
| maximal normal subgroup of | #11712273, #11712275, #11712308, … |
| maximal quotient of | #11712369, #11712377, #11712383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17980);