Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13161 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C2×D4 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C8×D4 |
| prime radical | C23×C17 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C22×C16×C17 ◁ G | |
298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,27,33,28,32,42,48,29,34,41,31,26,43,25,40)(24,30,37,46,38,45,51,53,39,47,50,44,36,52,35,49);(19,21)(22,24,27,37,28,38,42,51,29,39,41,50,26,36,25,35)(23,30,33,46,32,45,48,53,34,47,31,44,43,52,40,49);(22,25,26,41,29,42,28,27)(23,31,32,40,34,33,43,48)(24,35,36,50,39,51,38,37)(30,44,45,49,47,46,52,53)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6149);