Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2388 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Frattini | C23 | C23×D17 |
| Fitting | C4×C22⋊C4×C17 | C2 |
| hypercenter | C4×C22⋊C4 | D17 |
| hypocenter | C17 | #2388 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
944 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^16,h^c=h^16364 conjugacy classes — view the full character table.
| maximal subgroup of | #16929292, #16929297, #17006432, … |
| maximal normal subgroup of | #16929292, #16929297, #17006432, … |
| maximal quotient of | #16956004, #16956007, #16956037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7726);