Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #3407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#3633 |
| commutator, socle | C2×C17 | C23×C8 |
| Fitting | #41×C17 | C8 |
| prime radical | #41×D17 | C4 |
| cosocle | #3624 | C24 |
| hypercenter | #41 | #3633 |
| hypocenter | C17 | #3407 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ #41 | |
360 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=e,e^2=f,f^2=g,d^a=dg,h^a=h^9,c^b=cg,h^d=h^16,h^e=h^13,h^f=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | #17982580, #17982581, #17982594, … |
| maximal normal subgroup of | #17982580, #17982581, #17982594, … |
| maximal quotient of | #17983014, #17983020, #17983021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21764);