Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #2855 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting | C22×C42×C17 | C2 |
| prime radical | C24×C17 | C23 |
| hypercenter | C22×C42 | D17 |
| hypocenter | C17 | #2855 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C22×C42 | |
564 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 189 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=e,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^16556 conjugacy classes — view the full character table.
| maximal subgroup of | #16922659, #16922662, #16922687, … |
| maximal normal subgroup of | #16922659, #16922662, #16922687, … |
| maximal quotient of | #16965508, #16965546, #16965568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 12849);