Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5×C11 |
| 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 ⋊ (C5⋊D5)⋊C3 |
| Hall | C5⋊D5 ⋊ C112⋊C3 |
| 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 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 165 |
Polycyclic presentation:
2,3,5^2,11^2|c^a=c^4,d^a=d^4,c^b=cd^3,d^b=c^4d^3,e^b=e^3f^9,f^b=ef^7570 conjugacy classes — view the full character table.
| maximal subgroup of | #49137556, #49137563, #1043⋊(C112⋊C3), … |
| maximal normal subgroup of | #49137556, #49137563, #1043⋊(C112⋊C3), … |
| maximal quotient of | #1039⋊(C112⋊C3), C2×(C5⋊D5)⋊(C112⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 177);