Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3323 |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3)(6,11)(8,10)(13,19)(17,25)(18,20)(24,26);(13,18)(14,21)(16,23)(17,24)(19,20)(25,26);(4,6)(5,8)(7,11)(9,10)(12,14)(13,17)(15,21)(16,22)(18,26)(19,25)(20,24)(23,27);(2,3)(4,5,7,9)(6,10,11,8)(12,13,15,19)(14,17,21,25)(16,18,23,20)(22,26,27,24)Polycyclic presentation:
2^7,3|a^2=e,f^2=g,b^a=beg,c^a=cf,d^a=dg,f^a=fg,h^a=h^2,c^b=cg,d^b=deg,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3323, C2×#83501, #11672136, … |
| maximal normal subgroup of | D3×#3323, C2×#83501, #11672136, … |
| maximal quotient of | #10810787, #10811589, #10812472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16077);