Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5×C11 |
| direct product | C5⋊D5×C112⋊C3 |
| unambiguous semidirect product | C5⋊(D5×C112⋊C3) |
| Fitting, socle, derived, Hall | C52×C112 ⋊ C2×C3 |
| Hall | C52×C112⋊C3 ⋊ C2 |
| Hall | C112×C5⋊D5 ⋊ C3 |
| Sylow | C112 ⋊ C3×C5⋊D5 |
| Sylow | C52 ⋊ C2×C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C112 | C2×C3 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 825 |
602 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D52×C112⋊C3, #49137605, ((C5⋊D5)⋊(C11⋊D11))⋊C3, … |
| maximal normal subgroup of | D52×C112⋊C3, #49137605, ((C5⋊D5)⋊(C11⋊D11))⋊C3, … |
| maximal quotient of | #1039×C112⋊C3, C2×C5⋊D5×C112⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 168);