Finite Group DatabasebetaFinite Group Databasebeta| order | 2852 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C23×D31 |
| unambiguous semidirect product | C31⋊(C22×C23) |
| unambiguous semidirect product | (C2×C31)⋊(C2×C23) |
| Fitting, socle | C2×C23×C31 ⋊ C2 |
| derived, Sylow | C31 ⋊ C22×C23 |
| Hall | C23×C31 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D31 |
| commutator, cosocle, hypocenter | C31 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C23×C31 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C23 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1426 |
782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C23×D31⋊C5, D5×C23×D31, C2×C23×D155, … |
| maximal normal subgroup of | C2×C23×D31⋊C5, C2×C5×C23×D31, C2×C7×C23×D31, … |
| maximal quotient of | D5×C23×D31, C2×C23×D155, C2×C5×C23×D31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2852, 9);