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.
93 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,3,4,7,5,8,2,6)(9,17,22)(10,15,24,14,21,23)(11,12,20)(16,19);(1,2,5,4)(3,7,8,6)(9,10,11,14)(12,19,17,16)(13,21,18,15)(20,24,22,23)Polycyclic presentation:
2^4,3,2^3|a^2=d,b^2=c,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 | C2×#73009, #11711845, #11711846, … |
| maximal normal subgroup of | C2×#73009, #11711845, #11711846, … |
| maximal quotient of | #11711002, #11711087, #11711106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5585);