Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of A4×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | A4×C5⋊D5 |
| unambiguous semidirect product | C5⋊(D5×A4) |
| Fitting, socle, derived | C22×C52 ⋊ C2×C3 |
| Hall | C22×C5⋊D5 ⋊ C3 |
| Sylow | C52 ⋊ C2×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C52 | C2×C3 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | A4⋊#1043, A4⋊#1044, A4×#1043, … |
| maximal normal subgroup of | A4⋊#1043, A4⋊#1044, A4×#1043, … |
| maximal quotient of | C5⋊(C5⋊(#41⋊C3)), SL(2,𝔽3)×C5⋊D5, A4×#1039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 182);