Finite Group DatabasebetaFinite Group Databasebeta| order | 2300 |
| isoclinism | isoclinic class of D5×D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×D23 |
| unambiguous semidirect product | (D5×C23)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D23)⋊(C2×C5) |
| unambiguous semidirect product | D115⋊(C2×C5) |
| Fitting, socle, Hall | C52×C23 ⋊ C22 |
| derived | C5×C23 ⋊ C22×C5 |
| Sylow | C52 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×D23 |
| commutator, cosocle, hypocenter | C5×C23 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C23 | C22 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 230 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D5×D23, C5×D23×D35, C5×D5×D161, … |
| maximal normal subgroup of | C5×C7×D5×D23, C5×D5×AGL(1,𝔽23), C5×D5×C11×D23, … |
| maximal quotient of | C5×C7×D5×D23, C5×D23×D35, C5×D5×D161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2300, 21);