Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2202 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#2203 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C23×C17 |
| prime radical | C17×#454 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×Q8×C17 ◁ G | |
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,29)(21,33)(22,25)(23,28)(24,30)(26,36)(27,38)(31,46)(32,44)(34,42)(35,43)(37,47)(39,45)(40,48)(41,49);(18,20,23,32)(19,24,28,42)(21,34,36,30)(22,37,38,31)(25,40,27,41)(26,44,33,29)(35,48,39,49)(43,46,45,47);(19,25)(22,38)(24,40)(26,45)(27,28)(29,46)(31,37)(33,43)(35,39)(41,42)(44,47)(48,49)289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 935);