Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C17 ⋊ #2406 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting, prime radical | C22×#41×C17 | C2 |
| hypercenter | C22×#41 | D17 |
| hypocenter | C17 | #2406 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
864 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 185 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|b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^16358 conjugacy classes — view the full character table.
| maximal subgroup of | #16932125, #16932145, #16932311, … |
| maximal normal subgroup of | #16932125, #16932145, #16932311, … |
| maximal quotient of | #16956211, #16957013, #16957101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7841);