Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C23 · Schur multiplier (H2) = C29 |
| direct product | C23×#585 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | C24 |
| commutator, Frattini, cosocle | C2 | C25×C23 |
| socle | C2×C23 | C25 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ G | |
810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 368 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25)(26,32)(27,31)(28,30)(29,33)(34,38)(35,37)(36,39);(24,26)(25,29)(27,34)(28,33)(30,32)(31,36)(35,39)(37,38);(26,33)(29,32)(34,39)(36,38);(25,30)(29,32)(31,37)(36,38);(24,27,28,35)(25,31,30,37)(26,34,33,39)(29,36,32,38)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 266);