Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C17 ⋊ C8 |
| Sylow | C17 ⋊ #2988 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#3633 |
| commutator, socle | C2×C17 | C23×C8 |
| Fitting | #41×C17 | C8 |
| prime radical | #41×D17 | C4 |
| cosocle | C2×#595 | C24 |
| hypercenter | #41 | #3633 |
| hypocenter | C17 | #2988 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ #41 | |
432 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 191 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,d^2=e,f^2=g,b^a=be,d^a=de,h^a=h^9,c^b=ce,h^f=h^13,h^g=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | #17981695, #17981696, #17981710, … |
| maximal normal subgroup of | #17981695, #17981696, #17981710, … |
| maximal quotient of | #17982889, #17982890, #17982891, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21754);