Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C8×D4 ⋊ C2 |
| Sylow | C3 ⋊ #3285 |
482 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2)(8,10,12,16)(9,14,15,23)(11,21,19,18)(13,22,20,17);(5,7);(2,3)(8,9,12,15)(10,17,16,22)(11,20,19,13)(14,21,23,18);(2,3)(4,5)(6,7)(9,13)(10,16)(11,19)(14,17)(15,20)(22,23)Polycyclic presentation:
2^7,3|b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^2,d^b=de,e^b=eg,h^b=h^2,e^d=eg,h^d=h^275 conjugacy classes — view the full character table.
| maximal subgroup of | #10951656, #10951665, #10951716, … |
| maximal normal subgroup of | #10951656, #10951665, #10951716, … |
| maximal quotient of | #10785736, #10785751, #10785766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12020);