Finite Group DatabasebetaFinite Group Databasebeta| order | 22300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C223 · Schur multiplier (H2) = C5 |
| direct product | #1039×C223 |
| derived, Sylow | C52 ⋊ C4×C223 |
| Hall | C52×C223 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C223 | C5⋊D5 |
| commutator, hypocenter | C52 | C4×C223 |
| Frattini | C2 | C5⋊D5×C223 |
| Fitting, socle, prime radical | C2×C52×C223 | C2 |
| cosocle | C2×C52 | C2×C223 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C223 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22300 |
6244 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22300, 14);