Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C67 ⋊ #14639 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D67 |
| commutator | C23×C67 | C23×C4 |
| Fitting | C67×#1444 | C2 |
| socle, prime radical, cosocle | C24×C67 | C24 |
| hypercenter | #1444 | D67 |
| hypocenter | C67 | #14639 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ #1444 | |
1074 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17152 |
Polycyclic presentation:
2^8,67|a^2=h,b^2=eg,c^2=g,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,i^b=i^66,d^c=de,i^c=i^66,i^d=i^661504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 100386);