Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C17 ⋊ #2782 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting | C17×#394 | C2 |
| prime radical | C22×D4×C17 | C22 |
| hypercenter | #394 | D17 |
| hypocenter | C17 | #2782 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #394 | |
448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 448 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=efg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=def,h^a=h^16,c^b=cg,d^b=de,h^c=h^16208 conjugacy classes — view the full character table.
| maximal subgroup of | #16946652, #16946656, #16947238, … |
| maximal normal subgroup of | #16946652, #16946656, #16947238, … |
| maximal quotient of | #16962130, #16962562, #16962916, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 12188);