Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#2229 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ C4×C8×C17 ◁ G | |
124 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,23)(20,24,25,22)(26,27,29,32)(28,36,37,54)(30,42,40,55)(31,45,41,35)(33,49,47,38)(34,51,48,44)(39,56,46,52)(43,53,57,50);(18,20,21,25)(19,22,23,24)(27,32)(33,47)(34,48)(35,45)(36,54)(42,55)(50,53)(52,56);(26,28,29,37)(27,33,32,47)(30,43,40,57)(31,46,41,39)(34,52,48,56)(35,53,45,50)(36,55,54,42)(38,51,49,44)493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 961);