Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #73011 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×Q8 ⋊ D3 |
131 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,2,6,8,4,7,3,5)(9,15,16)(10,14,12);(2,5)(3,6)(7,8)(10,13)(11,15)(14,16)Polycyclic presentation:
2^4,3,2^3|b^2=cd,c^2=d,f^2=h,g^2=h,b^a=bc,c^a=cd,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh37 conjugacy classes — view the full character table.
| maximal subgroup of | #11711453, #11711454, #11711457, … |
| maximal normal subgroup of | #11711453, #11711454, #11711457, … |
| maximal quotient of | #11711071, #11711183, #11711470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5598);