Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C34 · Schur multiplier (H2) = C23×C37 |
| direct product | C23×C32×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C33 | C32 |
| commutator, Frattini, cosocle | C3 | C23×C34 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C23×C33 ◁ G | |
7200 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 648 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(7,8,9);(3,4)(10,11,12);(5,6)(13,14,16)(15,18,20)(17,21,19);(14,17,18)(16,20,21)792 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3777);