Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
125 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 36 points:
(5,29,33,24,8,28,7,30,21,6,16,35,10,13,34,11,20,31,12,22,19,15,25,36)(9,14,26,27,18,32,17,23);(1,2,3,4)(6,11)(7,12)(8,18)(9,20)(13,27)(14,30)(15,24)(16,17)(19,21)(22,32)(23,29)(25,26)(28,36)(31,35)Polycyclic presentation:
2^4,3,2^3|a^2=c,b^2=dh,d^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh40 conjugacy classes — view the full character table.
| maximal subgroup of | #11711521, #11711522, #11711540, … |
| maximal normal subgroup of | #11711521, #11711522, #11711540, … |
| maximal quotient of | #11711069, #11711071, #11711072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5702);