Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#544 ⋊ C2 |
| Sylow | C3 ⋊ #3084 |
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3)(12,14,15,21)(13,18,19,25)(16,22,23,27)(17,24,20,26);(2,3)(13,17)(16,23)(18,24)(19,20)(22,27)(25,26);(4,6,7,11)(5,8,9,10)(14,21)(18,25)(22,27)(24,26);(4,5,7,9)(6,10,11,8)(12,13,15,19)(14,18,21,25)(16,17,23,20)(22,24,27,26)Polycyclic presentation:
2^7,3|a^2=e,b^2=eg,d^2=g,f^2=g,b^a=beg,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10852726, #10852729, #10852735, … |
| maximal normal subgroup of | #10852726, #10852729, #10852735, … |
| maximal quotient of | #10794710, #10796190, #10796228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16052);