Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#60819 |
| 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 ◁ C4×#41×C17 ◁ G | |
2058 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(18,19)(20,24)(21,23)(22,25)(26,27)(28,37)(29,41)(30,35)(31,33)(32,38)(34,42)(36,44)(39,46)(40,45)(43,49)(47,52)(48,54)(50,51)(53,56)(55,57);(18,20,21,25)(19,22,23,24)(26,28)(27,32)(29,39)(30,38)(31,40)(33,47)(34,46)(35,37)(36,45)(41,50)(42,51)(43,53)(44,52)(48,56)(49,55)(54,57);(20,25)(22,24)(27,33)(28,38)(31,44)(32,45)(34,48)(35,36)(37,47)(39,51)(41,49)(43,54)(46,55)(50,56);(19,23)(22,24)(26,29)(27,34)(28,39)(30,42)(31,43)(32,46)(33,48)(35,41)(36,49)(37,50)(38,51)(40,53)(44,54)(45,55)(47,56)(52,57);(29,42)(34,41)(39,51)(43,54)(46,50)(48,49)(53,57)(55,56)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53807);