Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17687 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3512 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×#41×C17 ◁ G | |
896 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,27,23,26,21,25)(20,28,29,33,30,24,31,32)(35,39,41,44)(40,46,47,49);(18,20)(19,24)(21,29)(22,31)(23,30)(25,32)(26,28)(27,33)(34,35)(36,40)(37,44)(38,41)(39,45)(42,47)(43,49)(46,48);(18,21,23,22)(19,25,26,27)(20,29,30,31)(24,32,28,33)(34,36)(35,40)(37,43)(38,42)(39,46)(41,47)(44,49)(45,48);(18,21,23,22)(19,25,26,27)(20,29,30,31)(24,32,28,33)(36,42)(40,47)(43,48)(46,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10675);