Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#36743 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C17×#2671 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2064 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(24,28)(27,29)(30,31)(32,38)(33,37)(34,35)(36,40)(39,44)(41,42)(43,45);(23,26)(27,29)(31,35)(36,38)(37,42)(43,44);(18,19,20,21)(22,23)(24,27)(25,26)(28,29)(30,31)(32,36)(33,37)(34,35)(38,40)(39,43)(41,42)(44,45);(22,23)(24,27)(25,26)(28,29)(30,32)(31,36)(33,39)(34,40)(35,38)(37,43)(41,45)(42,44);(22,24)(23,27)(25,28)(26,29)(30,33,34,41)(31,37,35,42)(32,39,40,45)(36,43,38,44)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29731);