Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12725 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12725 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1782 |
| commutator | C24 | C22×C4×C17 |
| Frattini, cosocle | C22×D4 | C23×C17 |
| prime radical | C17×#3490 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C23×C17 ◁ C17×#518 ◁ G | |
846 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)(20,26)(21,29,30,23)(22,25)(24,28)(27,31,33,32);(19,23)(24,31)(25,29)(26,32);(18,20)(19,24,25,26)(21,27)(22,28)(23,31,29,32)(30,33)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5713);