Finite Group DatabasebetaFinite Group Databasebeta| order | 6100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1039 |
| Sylow | C52 ⋊ #6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C61 | C4 |
| LCS | G ▷ C52×C61 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,61|a^2=b,c^a=c^4,d^a=d^4,e^a=e^50,e^b=e^60403 conjugacy classes — view the full character table.
| maximal subgroup of | #32913039, #32913060, #32913062, … |
| maximal normal subgroup of | #32913039, #32913060, #32913062, … |
| maximal quotient of | C3×#20259124, C3⋊#20259124 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6100, 61);