Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C42×D4×C67 ⋊ C2 |
| Sylow | C67 ⋊ #34597 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D67 |
| commutator, socle, cosocle | C23×C67 | C25 |
| Frattini | C23 | C24×D67 |
| Fitting | C42×D4×C67 | C2 |
| hypercenter | C42×D4 | D67 |
| hypocenter | C67 | #34597 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C42×D4 | |
1940 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8576 |
Polycyclic presentation:
2^8,67|a^2=f,d^2=f,e^2=fg,b^a=bf,c^a=cg,d^a=dh,i^a=i^66,c^b=ch2704 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 336472);