Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C24×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1779 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#3633 |
| commutator, socle | C22×C17 | C22×C8 |
| Fitting | C24×C17 | C8 |
| prime radical | C24×D17 | C4 |
| cosocle | C22×#595 | C23 |
| hypercenter | C24 | #3633 |
| hypocenter | C17 | #1779 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C24 | |
852 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^7,17|a^2=f,f^2=g,b^a=bd,c^a=ce,h^a=h^9,h^f=h^13,h^g=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | #17981086, #17981638, #17981639, … |
| maximal normal subgroup of | #17981086, #17981638, #17981639, … |
| maximal quotient of | #17981638, #17981639, #17981640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21649);