Finite Group DatabasebetaFinite Group Databasebeta| order | 2300 |
| isoclinism | isoclinic class of D23×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | D23×C5⋊D5 |
| unambiguous semidirect product | (C5×D23)⋊D5 |
| Fitting, socle, derived, Hall | C52×C23 ⋊ C22 |
| Sylow | C52 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C23 | C22 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 575 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | C7×D23×C5⋊D5, D23×C5⋊D35, C5⋊D5×D161, … |
| maximal normal subgroup of | C7×D23×C5⋊D5, C5⋊D5×AGL(1,𝔽23), C11×D23×C5⋊D5, … |
| maximal quotient of | C7×D23×C5⋊D5, D23×C5⋊D35, C5⋊D5×D161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2300, 28);