Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61492 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#529 ◁ G | |
1770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(23,25)(26,27)(28,33)(29,41)(30,35)(31,45)(32,36)(34,43)(37,53)(38,48)(39,49)(40,55)(42,57)(44,51)(46,52)(47,54)(50,56);(18,19)(20,23)(21,22)(24,25)(26,28)(27,33)(29,42)(30,38)(31,40)(32,39)(34,50)(35,48)(36,49)(37,44)(41,57)(43,56)(45,55)(46,54)(47,52)(51,53);(26,29)(27,34)(28,37)(30,43)(31,46)(32,44)(33,47)(35,51)(36,52)(38,54)(39,42)(40,56)(41,45)(48,57)(49,50)(53,55);(19,22)(23,25)(26,30,32,31)(27,35,36,45)(28,38,39,40)(29,43,44,46)(33,48,49,55)(34,51,52,41)(37,54,42,56)(47,57,50,53);(18,20,21,24)(19,23,22,25)(28,39)(33,49)(37,42)(38,40)(47,50)(48,55)(53,57)(54,56)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54480);