Finite Group DatabasebetaFinite Group Databasebeta| order | 920 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×D20 |
| unambiguous semidirect product | C4⋊(D5×C23) |
| Fitting | C4×C5×C23 ⋊ C2 |
| Hall | C5×C23 ⋊ D4 |
| Sylow | C5 ⋊ D4×C23 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C23 | C2×D5 |
| commutator, cosocle | C2×C5 | C22×C23 |
| Frattini | C2 | C2×D5×C23 |
| Fitting | C4×C5×C23 | C2 |
| socle | C2×C5×C23 | C22 |
| hypercenter | C4×C23 | D5 |
| hypocenter | C5 | D4×C23 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C23 ◁ C4×C23 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 460 |
299 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14270230, #14270232, #14270234, … |
| maximal normal subgroup of | #14270230, #14270232, #14270234, … |
| maximal quotient of | C23×#677, C23×D40, C23×Dic20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(920, 21);