Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×#2846 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C3 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ G | |
3422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14,15);(2,4);(6,8);(10,12)132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17286);