Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #10597198⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #10597198⋊C2 |
| unambiguous semidirect product | ((C5⋊D5)⋊A4)⋊C2 |
| Fitting, socle | C22×C52 ⋊ C2×D3 |
| derived | C22⋊(C52⋊C3) ⋊ C22 |
| Sylow | C52 ⋊ C2×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22⋊(C52⋊C3) | C22 |
| Fitting, socle | C22×C52 | C2×D3 |
| LCS | G ▷ C22⋊(C52⋊C3) | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
Polycyclic presentation:
2^2,3,2^2,5^2|c^a=c^2,d^a=de,f^a=f^4g^4,f^b=f^4,g^b=g^4,d^c=e,e^c=de,f^c=g,g^c=f^4g^430 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 985);