Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
192 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 40 points:
(2,6)(5,8)(9,33,23,19,24,38,14,20,26,11,12,36)(10,37,31,28,25,40,18,29,32,15,16,39)(13,21,27,34)(17,30,22,35);(1,3,4,7)(2,5,6,8)(11,19)(15,28)(20,33)(21,34)(29,37)(30,35)(36,38)(39,40);(1,2)(3,5)(4,6)(7,8)(9,10,14,18)(11,15,19,28)(12,22,24,17)(13,25,27,16)(20,35,33,30)(21,37,34,29)(23,32,26,31)(36,40,38,39)Polycyclic presentation:
2^4,3,2^3|a^2=h,b^2=d,c^2=h,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 | C2×#85362, #11714815, #11714821, … |
| maximal normal subgroup of | C2×#85362, #11714815, #11714821, … |
| maximal quotient of | #11712667, #11712780, #11712783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17938);