Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#1270 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22⋊C4 |
| commutator | C2×C4 | C2×C8×C17 |
| Frattini, cosocle | C2×C42 | C22×C17 |
| prime radical | C22×D4×C17 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
202 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24,25,22)(21,23)(26,27)(28,30)(29,32)(31,33)(34,35,36,38,37,39,40,41);(18,20)(19,22)(21,25)(23,24)(27,30)(28,33)(31,32)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2);