Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11521 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12719 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #410 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| socle | C2×C17 | #1782 |
| prime radical | C17×#3444 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C42×C17 ◁ C4×#41×C17 ◁ G | |
780 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,27,29,23)(21,25)(22,26)(24,28,31,33)(30,32);(19,23)(24,25)(26,27)(31,32);(18,20)(19,24,26,31)(21,28)(22,29)(23,25,27,32)(30,33)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5707);