Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×C8×D4 ⋊ C2 |
| Sylow | C3 ⋊ #3337 |
354 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)(9,10);(2,3)(4,7,8,5)(6,10,11,9)(13,18)(16,23)(17,24)(19,20)(22,27)(25,26);(4,6)(5,9)(7,10)(8,11)(12,14,15,21)(13,17,19,25)(16,22,23,27)(18,24,20,26);(2,3)(4,5,8,7)(6,10,11,9)(12,13,15,19)(14,17,21,25)(16,18,23,20)(22,24,27,26)Polycyclic presentation:
2^7,3|a^2=e,b^2=g,c^2=eg,f^2=g,b^a=beg,c^a=cf,f^a=fg,h^a=h^2,d^b=deg,f^c=fg,h^c=h^275 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3337, C2×#79414, #11673695, … |
| maximal normal subgroup of | D3×#3337, C2×#79414, #11673695, … |
| maximal quotient of | #10811414, #10811440, #10812807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11990);