Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
199 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,3,4,8)(2,5,6,7)(9,19,20)(10,15,24,14,21,23)(11,18,13)(16,22);(9,10,13,14)(11,15,19,21)(12,16,17,22)(18,23,20,24);(1,2,4,6)(3,7,8,5)(11,17)(12,19)(15,22)(16,21)(18,20)(23,24)Polycyclic presentation:
2^4,3,2^3|a^2=d,b^2=h,c^2=d,f^2=h,g^2=h,c^a=cd,e^a=e^2,f^a=gh,g^a=fh,c^b=ch,f^e=g,g^e=fgh,g^f=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | #11713751, #11713752, #11713754, … |
| maximal normal subgroup of | #11713751, #11713752, #11713754, … |
| maximal quotient of | #11712639, #11712696, #11712699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17937);