Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C17×#399 ⋊ C2 |
| Sylow | C17 ⋊ #2820 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting | C17×#399 | C2 |
| prime radical | C22×C22⋊D17 | C22 |
| hypercenter | #399 | D17 |
| hypocenter | C17 | #2820 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #399 | |
464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 125 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=ef,b^2=e,d^2=e,b^a=be,c^a=cf,h^a=h^16,c^b=cg,d^b=def,d^c=de,h^d=h^16202 conjugacy classes — view the full character table.
| maximal subgroup of | #17009843, #17009845, #17009854, … |
| maximal normal subgroup of | #17009843, #17009845, #17009854, … |
| maximal quotient of | #16964998, #16965020, #16965039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 12564);