Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25409 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3153 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(22,23,27,31,26,30,33,43)(24,32,36,49,35,28,42,45)(25,37,40,47,39,48,41,29)(34,50,51,44,38,53,52,46);(18,19,21,20)(22,24,33,42,26,35,27,36)(23,28,43,49,30,32,31,45)(25,38,41,51,39,34,40,52)(29,46,48,53,47,44,37,50);(22,25,26,39)(23,29,30,47)(24,34,35,38)(27,41,33,40)(28,44,32,46)(31,48,43,37)(36,52,42,51)(45,50,49,53);(18,20,21,19)(23,30)(28,32)(29,47)(31,43)(37,48)(44,46)(45,49)(50,53)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18397);