Finite Group DatabasebetaFinite Group Databasebeta| order | 1972 |
| isoclinism | isoclinic class of #14520307 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C17×C29 ⋊ C4 |
| Sylow | C29 ⋊ #595 |
| Sylow | C17 ⋊ #1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C29 | C4 |
| prime radical, cosocle | D493 | C2 |
| LCS | G ▷ C17×C29 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 493 |
Polycyclic presentation:
2^2,17,29|a^2=b,c^a=c^13,d^a=d^12,c^b=c^16,d^b=d^28127 conjugacy classes — view the full character table.
| maximal subgroup of | #14520307⋊C7, C7×#14520307, C7⋊#14520307, … |
| maximal normal subgroup of | #14520307⋊C7, C7×#14520307, C11×#14520307, … |
| maximal quotient of | C7×#14520307, C7⋊#14520307, #31801694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1972, 7);