Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #2930 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D17 |
| commutator, socle | C22×C17 | C23×C4 |
| Fitting, prime radical | C17×#525 | C2 |
| cosocle | C2×C4×C17 | C24 |
| hypercenter | #525 | D17 |
| hypocenter | C17 | #2930 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^a=h^16,c^b=cg,h^c=h^16268 conjugacy classes — view the full character table.
| maximal subgroup of | #16949484, #16950342, #17040186, … |
| maximal normal subgroup of | #16949484, #16950342, #17040186, … |
| maximal quotient of | #17004517, #17004526, #17004535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 13214);