Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
211 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 24 points:
(3,7)(5,8)(9,23,18,16,19,24,13,14,20,10,11,22)(12,15,17,21);(1,3)(2,5)(4,7)(6,8);(1,2,4,6)(3,5,7,8)(11,17)(12,19)(14,21)(15,23)(18,20)(22,24)Polycyclic presentation:
2^4,3,2^3|a^2=d,c^2=h,f^2=h,g^2=h,e^a=e^2,f^a=gh,g^a=fh,c^b=cd,f^e=g,g^e=fgh,g^f=gh40 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#85375, #11715009, #11715027, … |
| maximal normal subgroup of | C2×#85375, #11715009, #11715027, … |
| maximal quotient of | #11712904, #11712989, #11712990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17951);