Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | SL(2,𝔽3) ⋊ C2×C8 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 24 points:
(9,21,18,14,19,24,13,15,20,10,11,23)(12,16,17,22);(1,2,3,5,4,6,7,8)(10,14)(11,17)(12,19)(15,16)(18,20)(21,22)Polycyclic presentation:
2^4,3,2^3|a^2=c,b^2=h,c^2=d,f^2=h,g^2=h,b^a=bh,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh52 conjugacy classes — view the full character table.
| maximal subgroup of | #11711015, #11711016, #11711041, … |
| maximal normal subgroup of | #11711015, #11711016, #11711041, … |
| maximal quotient of | #11710987, #11711014, C4⋊(SL(2,𝔽3)⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5647);