Finite Group DatabasebetaFinite Group Databasebeta| order | 29100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C52×C97 ⋊ Dic3 |
| derived, Hall | C52⋊C3×C97 ⋊ C4 |
| Sylow | C97 ⋊ #64470 |
| Hall | C52⋊C3 ⋊ #87604 |
| Sylow | C52 ⋊ C3⋊#87604 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C52⋊C3×C97 | C4 |
| Fitting, socle | C52×C97 | Dic3 |
| prime radical, cosocle | C52⋊C3×D97 | C2 |
| LCS | G ▷ C52⋊C3×C97 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1455 |
Polycyclic presentation:
2^2,3,97,5^2|a^2=b,c^a=c^2,d^a=d^75,e^a=ef^2,f^a=f^4,d^b=d^96,e^c=e^3f^3,f^c=e^4f290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29100, 84);