Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#452 ⋊ C2 |
| Sylow | C3 ⋊ #3210 |
394 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)(5,9)(8,10)(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21);(6,11)(8,10)(12,14)(13,18)(15,22)(16,25)(17,23)(19,26)(20,27)(21,24);(2,3)(4,6,7,11)(5,8,9,10);(4,5)(6,10)(7,9)(8,11)(12,13,17,20)(14,21,23,26)(15,19,16,24)(18,25,27,22)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,h^b=h^2,f^c=fg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3210, C2×#80220, #11666418, … |
| maximal normal subgroup of | D3×#3210, C2×#80220, #11666418, … |
| maximal quotient of | #10804503, #10804898, #10805720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12796);