Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
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:
(1,3,5,4)(2,6,7,8)(9,21,19,14,17,24,11,15,20,10,12,23)(13,16,18,22);(1,2,4,6,5,7,3,8)(10,14)(12,18)(13,17)(15,16)(19,20)(21,22)Polycyclic presentation:
2^4,3,2^3|a^2=c,b^2=d,c^2=dh,f^2=h,g^2=h,b^a=bd,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh46 conjugacy classes — view the full character table.
| maximal subgroup of | #11711051, #11711052, #11711059, … |
| maximal normal subgroup of | #11711051, #11711052, #11711059, … |
| maximal quotient of | #11710988, #11711014, C4⋊(SL(2,𝔽3)⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5648);