Finite Group DatabasebetaFinite Group Databasebeta| order | 10900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C109 ⋊ C4 |
| Sylow | C109 ⋊ #1039 |
| Sylow | C52 ⋊ #89137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C109 | C4 |
| prime radical, cosocle | C52×D109 | C2 |
| LCS | G ▷ C52×C109 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,109|a^2=b,c^a=c^4,d^a=d^4,e^a=e^76,e^b=e^108703 conjugacy classes — view the full character table.
| maximal subgroup of | #45658250, #45658252, #45658282, … |
| maximal normal subgroup of | #45658250, #45658252, #45658282, … |
| maximal quotient of | C3×#24926280, C3⋊#24926280 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10900, 41);