Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C17 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #3633 |
| commutator, hypocenter | C17 | C2×C64 |
| Frattini | C8 | C2×#3633 |
| Fitting | C16×C17 | C8 |
| socle | C2×C17 | C2×C32 |
| prime radical | C2×D17 | C32 |
| cosocle | #10587467 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C16 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^9,h^b=h^16,h^c=h^13,h^d=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #17981487, #17981490, C2×#14545887, … |
| maximal normal subgroup of | #17981487, #17981490, C2×#14545887, … |
| maximal quotient of | #17981486, #17981496, #17981502, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21613);