Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
209 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 209 conjugacy classes of subgroups — too many to draw. Only its 36 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:
(2,6)(5,8)(9,19,21)(10,15,24,14,20,23)(11,18,13)(16,17);(1,3,4,7)(2,5,6,8)(10,14)(15,20)(16,17)(23,24);(1,2)(3,5)(4,6)(7,8)(9,10,13,14)(11,17,19,16)(12,20,22,15)(18,24,21,23)Polycyclic presentation:
2^4,3,2^3|a^2=h,b^2=d,f^2=h,g^2=h,b^a=bh,c^a=cdh,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh40 conjugacy classes — view the full character table.
| maximal subgroup of | #11711169, #11711210, #11711990, … |
| maximal normal subgroup of | #11711169, #11711210, #11711990, … |
| maximal quotient of | #11712662, #11712778, #11712810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17895);