Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
298 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 36 points:
(2,4)(5,20,22)(6,21,28)(7,16,34,15,29,32)(8,19,10)(11,25,36,24,33,35)(12,27,14)(17,30)(26,31);(5,7)(6,11)(8,16)(9,17)(10,15)(12,25)(13,26)(14,24)(18,31)(19,32)(20,29)(21,33)(22,34)(23,30)(27,35)(28,36);(1,2)(3,4)(5,6,10,14)(7,11,15,24)(8,18,20,13)(9,21,23,12)(16,31,29,26)(17,33,30,25)(19,28,22,27)(32,36,34,35)Polycyclic presentation:
2^4,3,2^3|a^2=h,f^2=h,g^2=h,c^a=cd,e^a=e^2,f^a=gh,g^a=fh,c^b=ch,f^e=g,g^e=fgh,g^f=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | #11711618, #11711623, #11713365, … |
| maximal normal subgroup of | #11711618, #11711623, #11713365, … |
| maximal quotient of | #11712011, #11712014, #11712019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18111);