Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2395 |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(16,18,19,22)(17,21,20,23);(5,7)(9,13)(12,15);(2,3)(4,5)(6,7)(8,10,11,14)(9,12,13,15)(17,20)(21,23);(8,9)(10,12)(11,13)(14,15)(16,17)(18,21)(19,20)(22,23)Polycyclic presentation:
2^7,3|b^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10690164, #10690166, #10690169, … |
| maximal normal subgroup of | #10690164, #10690166, #10690169, … |
| maximal quotient of | #10716869, #10716884, #10716903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14922);