Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Sylow | C17 ⋊ #2641 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting, prime radical | C2×C17×#127 | C2 |
| hypercenter | C2×#127 | D17 |
| hypocenter | C17 | #2641 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=eg,b^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^16,c^b=cg,h^b=h^16,d^c=de256 conjugacy classes — view the full character table.
| maximal subgroup of | #16935670, #16935674, #16935726, … |
| maximal normal subgroup of | #16935670, #16935674, #16935726, … |
| maximal quotient of | #16960723, #16960847, #16960931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 10455);