Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#11597 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #102 |
| commutator | C8 | C22×C8×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C22×C17 | C2×#102 |
| prime radical | C2×C17×#135 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,22,21,23,24,25)(26,27)(28,37,40,54)(29,33)(30,44)(31,36)(32,39,48,56)(34,42)(35,43)(38,53,41,50)(45,52,57,47)(46,49)(51,55);(26,28)(27,32)(29,38)(30,45)(31,40)(33,47)(34,50)(35,52)(36,48)(37,49)(39,55)(41,43)(42,56)(44,54)(46,57)(51,53);(26,29,31,43)(27,33,36,35)(28,38,40,41)(30,42,46,55)(32,47,48,52)(34,49,51,44)(37,53,54,50)(39,45,56,57)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4585);