Finite Group DatabasebetaFinite Group Databasebeta| order | 18075 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊(C241⋊C3) |
| unambiguous semidirect product | C241⋊(C52⋊C3) |
| Fitting, socle, derived, Hall | C52×C241 ⋊ C3 |
| Sylow | C241 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ C241⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C241 | C3 |
| LCS | G ▷ C52×C241 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3615 |
Polycyclic presentation:
3,5^2,241|b^a=b^2c^3,c^a=bc^2,d^a=d^2252011 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D241⋊(C52⋊C3), #49116188, (C5⋊D5)⋊(C241⋊C3), … |
| maximal normal subgroup of | D241⋊(C52⋊C3), #49116188, (C5⋊D5)⋊(C241⋊C3), … |
| maximal quotient of | C2×C52⋊(C241⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18075, 8);