Finite Group DatabasebetaFinite Group Databasebeta| order | 6100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C25×C61 ⋊ C4 |
| Sylow | C61 ⋊ Dic25 |
| Sylow | C25 ⋊ #6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C61 | C4 |
| Frattini | C5 | #11927415 |
| socle | C5×C61 | Dic5 |
| LCS | G ▷ C25×C61 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,61,5|a^2=b,c^5=e^4,c^a=c^4e,d^a=d^50,e^a=e^4,d^b=d^60403 conjugacy classes — view the full character table.
| maximal subgroup of | #20259079⋊C3, C3×#20259079, C3⋊#20259079 |
| maximal normal subgroup of | #20259079⋊C3, C3×#20259079 |
| maximal quotient of | C3×#20259079, C3⋊#20259079 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6100, 16);