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 |
107 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 107 conjugacy classes of subgroups — too many to draw. Only its 20 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 — 2 generators on 24 points:
(1,2,6,8,4,7,3,5)(9,17,22)(10,15,24,14,21,23)(11,12,20)(16,19);(2,5)(3,6)(7,8)(9,10)(11,14)(12,19)(13,21)(15,18)(16,17)(20,24)(22,23)Polycyclic presentation:
2^4,3,2^3|b^2=cdh,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 | C2×#73024, #11712170, #11712172, … |
| maximal normal subgroup of | C2×#73024, #11712170, #11712172, … |
| maximal quotient of | #11711073, #11711181, #11711183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5600);