Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22×C8 |
| direct product | C17×#12515 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C17 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ C82×C17 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(20,23)(24,25)(27,31)(28,32)(29,35)(33,41)(34,39)(36,40)(37,38);(26,27,32,38,29,33,36,39,30,34,40,41,35,37,28,31);(18,19,23,25,21,24,20,22)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5503);