Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of #1043⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#1043⋊C3 |
| unambiguous semidirect product | (C2×#1043)⋊C3 |
| Fitting, socle | C2×C52 ⋊ C3×C4 |
| derived, Sylow | C52 ⋊ C2×C3×C4 |
| Hall | C2×#1043 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #1043⋊C3 |
| commutator, hypocenter | C52 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52 | C3×C4 |
| prime radical | C2×(C5⋊D5)⋊C3 | C2 |
| cosocle | C5⋊D5 | C22×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
28 conjugacy classes — view the full character table.
| maximal subgroup of | #64480⋊C4, #11925280, #11925281, … |
| maximal normal subgroup of | #64480⋊C4, #11925280, #11925281, … |
| maximal quotient of | #87855⋊C3, #87856⋊C3, C4×#1043⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 153);