Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28×C42 |
| direct product | C2×C17×#2309 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C24 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C24×D4×C17 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
7710 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(4,6)(7,8,9,10)(12,15)(13,17);(11,12,14,15)(13,16,17,18);(3,4)(5,6)(7,8)(9,10)(11,12)(13,16)(14,15)(17,18);(11,13)(12,16)(14,17)(15,18)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27029);