Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C22×#120×C67 ⋊ C2 |
| Sylow | C67 ⋊ #14715 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D67 |
| commutator, socle, cosocle | C24×C67 | C24 |
| Fitting | C22×#120×C67 | C2 |
| hypercenter | C22×#120 | D67 |
| hypocenter | C67 | #14715 |
| LCS | G ▷ C24×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C22×#120 | |
7490 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4288 |
Polycyclic presentation:
2^8,67|b^a=be,c^a=cf,d^a=dh,c^b=cg,i^c=i^661912 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 100942);