Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3252 |
348 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(2,3)(4,6,7,10)(5,9,8,11);(1,2,3)(5,8)(9,11)(13,18)(14,21)(15,23)(17,24)(19,20)(25,26);(4,5)(6,9)(7,8)(10,11)(12,14)(13,17)(15,22)(16,21)(18,26)(19,24)(20,25)(23,27);(5,8)(6,10)(12,13,16,20)(14,17,21,25)(15,18,23,19)(22,26,27,24)Polycyclic presentation:
2^7,3|a^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,f^c=fg,h^d=h^242 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3252, C2×#80793, #11668078, … |
| maximal normal subgroup of | D3×#3252, C2×#80793, #11668078, … |
| maximal quotient of | #10805108, #10805124, #10805580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13369);