Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C2×C42 |
| direct product | C17×#2832 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| prime radical | C22×D4×C17 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
416 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(23,25)(26,27)(28,30)(29,31)(32,33)(34,35,38,37)(36,39,40,41);(20,24)(23,25)(27,28)(31,32)(35,37)(39,41);(18,19)(20,23)(21,22)(24,25)(26,28,30,27)(29,31,33,32)(34,36,38,40)(35,39,37,41);(18,20)(19,23)(21,24)(22,25)(26,29,30,33)(27,31,28,32)(34,37,38,35)(36,39,40,41)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1564);