Finite Group DatabasebetaFinite Group Databasebeta| order | 10900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C109 ⋊ C4 |
| Sylow | C109 ⋊ #1043 |
| Sylow | C52 ⋊ Dic109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C109 | C4 |
| prime radical, cosocle | C5⋊D5×C109 | 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^2,d^a=d^2,e^a=e^108,c^b=c^4,d^b=d^4766 conjugacy classes — view the full character table.
| maximal subgroup of | #45658260, #45658264, #45658286, … |
| maximal normal subgroup of | #45658260, #45658264, #45658286, … |
| maximal quotient of | C3×#24926272, C3⋊#24926272 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10900, 33);