Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #1443 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D17 |
| commutator | C23×C17 | C22×C4 |
| Fitting | C2×C17×#95 | C2 |
| socle, prime radical, cosocle | C24×C17 | C23 |
| hypercenter | C2×#95 | D17 |
| hypocenter | C17 | #1443 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
476 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=de,c^2=d,b^a=bd,c^a=ce,h^a=h^16,c^b=cf364 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1443, C2×#14527046, #16956024, … |
| maximal normal subgroup of | D17×#1443, C2×#14527046, #16956024, … |
| maximal quotient of | #16922248, #16942772, #16942776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2772);