Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ #1446 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#595 |
| commutator, socle | C23×C17 | C22×C4 |
| Fitting | C22×Q8×C17 | C4 |
| prime radical, cosocle | C23×D17 | C23 |
| hypercenter | C22×Q8 | #595 |
| hypocenter | C17 | #1446 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
736 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=f,c^2=f,b^a=bd,c^a=ce,h^a=h^13,c^b=cf,h^g=h^16124 conjugacy classes — view the full character table.
| maximal subgroup of | #17949034, #17952852, #17952853, … |
| maximal normal subgroup of | #17949034, #17952852, #17952853, … |
| maximal quotient of | #17949634, #17957953, #17957954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19700);