Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of D48 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1371 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(12,13,18,24,15,19,22,25,16,20,26,27,21,23,14,17);(2,3)(4,5,6,8,7,9,10,11)(13,17)(14,18)(15,21)(19,27)(20,25)(22,26)(23,24)Polycyclic presentation:
2^7,3|a^2=d,b^2=ce,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #10682637, #10682638, #10682640, … |
| maximal normal subgroup of | #10682637, #10682638, #10682640, … |
| maximal quotient of | #10681927, #10682057, #10682864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 76);