Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C17 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×#595 |
| commutator, socle | C2×C17 | C24×C4 |
| Fitting | C17×2−1+4 | C4 |
| prime radical | #11763646 | C2 |
| cosocle | Dic17 | C25 |
| hypercenter | 2−1+4 | #595 |
| hypocenter | C17 | #3573 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
1424 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 750 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=f,f^2=g,h^a=h^13,e^b=eg,d^c=dg,h^c=h^16,h^d=h^16,h^f=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #17971223, #17971225, #17971227, … |
| maximal normal subgroup of | #17971223, #17971225, #17971227, … |
| maximal quotient of | #17979432, #17979433, #17979463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21506);