Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3585 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#3585 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C23×D4 |
| commutator, Frattini, cosocle | C4 | C25×C17 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×#41×C17 ◁ G | |
1464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,23)(22,25)(26,29)(27,31)(28,30)(32,33);(19,23)(21,29)(24,30)(25,26)(28,33)(31,32);(18,20)(19,24)(21,28)(22,27)(23,30)(25,31)(26,32)(29,33);(20,27)(24,31)(28,33)(30,32);(19,25)(23,26)(24,31)(30,32)697 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2317);