Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of A4×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | A4×D25 |
| unambiguous semidirect product | C25⋊(C2×A4) |
| unambiguous semidirect product | (C22×D25)⋊C3 |
| Fitting, derived | C22×C25 ⋊ C2×C3 |
| Hall | C22×D25 ⋊ C3 |
| Sylow | C25 ⋊ C2×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×C25 | C2×C3 |
| Frattini | C5 | D5×A4 |
| socle | C22×C5 | C3×D5 |
| LCS | G ▷ C22×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 100 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | A4⋊#1035, A4×#1035, S4×D25, … |
| maximal normal subgroup of | A4⋊#1035, A4×#1035, S4×D25, … |
| maximal quotient of | C25⋊(#41⋊C3), SL(2,𝔽3)×D25, A4×Dic25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 36);