Finite Group DatabasebetaFinite Group Databasebeta| order | 6100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊D5)⋊D61 |
| unambiguous semidirect product | D305⋊D5 |
| Fitting, socle, derived, Hall | C52×C61 ⋊ C22 |
| Sylow | C61 ⋊ D52 |
| Sylow | C52 ⋊ C2×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C61 | C22 |
| LCS | G ▷ C52×C61 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,61|c^a=c^4,e^a=e^60,c^b=c^4,d^b=d^4436 conjugacy classes — view the full character table.
| maximal subgroup of | (C5⋊(D61⋊C3))⋊D5, ((C5⋊D5)⋊C3)⋊D61, C3×(C5⋊D5)⋊D61, … |
| maximal normal subgroup of | (C5⋊(D61⋊C3))⋊D5, C3×(C5⋊D5)⋊D61 |
| maximal quotient of | C3×(C5⋊D5)⋊D61, D305⋊D15, #32913144 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6100, 65);