Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #73085 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
111 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 111 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) = 128 |
A minimal faithful permutation representation — 2 generators on 24 points:
(2,5)(3,8)(6,7)(9,15,19,10,20,23,14,17,21,11,12,24)(13,18,22,16);(1,2,4,7)(3,5,8,6)(9,10,14,11)(12,18,20,16)(13,17,22,15)(19,24,21,23)Polycyclic presentation:
2^4,3,2^3|a^2=dh,b^2=h,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,c^b=cd,f^e=g,g^e=fgh,g^f=gh31 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73090, #11711972, #11711979, … |
| maximal normal subgroup of | C2×#73090, #11711972, #11711979, … |
| maximal quotient of | #11711053, #11711095, #11711118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5666);