Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#12592 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C17 | C23 |
| commutator | C22 | C2×C4×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle, prime radical | C23×C17 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C17 ◁ G | |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23)(24,27)(25,26)(28,29)(30,31,33,37,34,38,43,49,35,39,44,50,45,51,55,59)(32,36,41,47,42,48,54,58,40,46,52,56,53,57,60,61);(18,19,20,21)(23,26)(27,29)(30,32)(31,36)(33,41)(34,42)(35,40)(37,47)(38,48)(39,46)(43,54)(44,52)(45,53)(49,58)(50,56)(51,57)(55,60)(59,61);(22,24,25,28)(23,27,26,29)(32,40)(36,46)(41,52)(42,53)(47,56)(48,57)(54,60)(58,61)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5580);