Finite Group DatabasebetaFinite Group Databasebeta| order | 10700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C107⋊#1043 |
| Fitting, socle, derived, Hall | C52×C107 ⋊ C4 |
| Sylow | C107 ⋊ #1043 |
| Sylow | C52 ⋊ Dic107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C107 | C4 |
| prime radical, cosocle | C5⋊D5×C107 | C2 |
| LCS | G ▷ C52×C107 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,107|a^2=b,c^a=c^2,d^a=d^2,e^a=e^106,c^b=c^4,d^b=d^4752 conjugacy classes — view the full character table.
| maximal subgroup of | C107⋊(#1043⋊C3), C3×C107⋊#1043, C3⋊(C107⋊#1043) |
| maximal normal subgroup of | C107⋊(#1043⋊C3), C3×C107⋊#1043 |
| maximal quotient of | C3×C107⋊#1043, C3⋊(C107⋊#1043) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10700, 23);