Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2659 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D3 |
| commutator, socle, cosocle | C23×C3 | C24 |
| Fitting | C3×#380 | C2 |
| prime radical | C24×C3 | C23 |
| hypercenter | #380 | D3 |
| hypocenter | C3 | #2659 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #380 | |
524 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)(10,14)(13,15);(5,7)(8,10)(9,13)(11,14)(12,15)(16,18,19,23)(17,20,21,22);(4,5,6,7)(9,12)(13,15);(2,3)(8,9)(10,13)(11,12)(14,15)(16,17,19,21)(18,22,23,20)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=f,b^a=be,c^a=cf,h^a=h^2,c^b=cg,d^c=de60 conjugacy classes — view the full character table.
| maximal subgroup of | #10698155, #10698156, #10698160, … |
| maximal normal subgroup of | #10698155, #10698156, #10698160, … |
| maximal quotient of | #10721728, #10721729, #10721730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6533);