Finite Group DatabasebetaFinite Group Databasebeta| order | 18975 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C5 |
| Fitting, socle, derived, Hall | C52×C23 ⋊ C3×C11 |
| Hall | C52×C23⋊C11 ⋊ C3 |
| Hall | C23×C52⋊C3 ⋊ C11 |
| Sylow | C52 ⋊ C3×C23⋊C11 |
| Sylow | C23 ⋊ C11×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C23 | C3×C11 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 345 |
143 conjugacy classes — view the full character table.
| maximal subgroup of | C52⋊C3×AGL(1,𝔽23), (C23⋊C11)⋊#3874, #3874×C23⋊C11, … |
| maximal normal subgroup of | C52⋊C3×AGL(1,𝔽23), (C23⋊C11)⋊#3874, #3874×C23⋊C11, … |
| maximal quotient of | C2×C52⋊C3×C23⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18975, 5);