Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
190 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,16,18)(2,9,26,7,17,24)(3,12,30,11,25,28)(4,15,6)(8,29,32)(10,14)(13,23)(20,21,31);(1,2,3,8,6,7,11,20)(4,14,12,27,16,10,25,22)(5,17,13,29,19,9,23,21)(15,26,28,32,18,24,30,31)Polycyclic presentation:
2^4,3,2^3|a^2=c,c^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,e^a=e^2,f^a=gh,g^a=fh,c^b=ch,f^e=g,g^e=fgh,g^f=gh31 conjugacy classes — view the full character table.
| maximal subgroup of | #11711508, #11711509, #11711623, … |
| maximal normal subgroup of | #11711508, #11711509, #11711623, … |
| maximal quotient of | #11711017, #11711028, #11711034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5730);