Finite Group DatabasebetaFinite Group Databasebeta| order | 18075 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×C241⋊C3 |
| Fitting, socle, Hall | C52×C241 ⋊ C3 |
| derived, Sylow | C241 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C241⋊C3 |
| commutator, cosocle, hypocenter | C241 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C241 | C3 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6025 |
2075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D241⋊C3, C5×C5⋊(D241⋊C3), C5×D5×C241⋊C3, … |
| maximal normal subgroup of | C52×D241⋊C3, C5×C5⋊(D241⋊C3), C5×D5×C241⋊C3, … |
| maximal quotient of | C2×C52×C241⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18075, 10);