Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of #1201 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#1201 |
| Hall | C3×C52 ⋊ D4 |
| Sylow | C52 ⋊ #67 |
| Sylow | C3 ⋊ C5×C22⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D3×D5 |
| commutator, cosocle | C2×C3×C5 | C22×C5 |
| Frattini | C2 | C5×D3×D5 |
| Fitting, socle | C2×C3×C52 | C22 |
| hypocenter | C3×C5 | C5×D4 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2×C5 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1201, #11925419, #11925423, … |
| maximal normal subgroup of | D5×#1201, #11925419, #11925423, … |
| maximal quotient of | C5×#6652, C5×#6655, C5×#6656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 88);