Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3327 |
380 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3)(6,11)(8,10)(13,18)(17,26)(19,24)(20,27);(12,14,15,21)(13,17,18,26)(16,25,23,22)(19,27,24,20);(4,6)(5,8)(7,11)(9,10)(14,21)(17,26)(20,27)(22,25);(2,3)(4,5,7,9)(6,10,11,8)(12,13,15,18)(14,20,21,27)(16,24,23,19)(17,25,26,22)Polycyclic presentation:
2^7,3|a^2=e,c^2=g,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×#3327, C2×#83541, #11672140, … |
| maximal normal subgroup of | D3×#3327, C2×#83541, #11672140, … |
| maximal quotient of | #10810813, #10811589, #10812487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16117);