Finite Group DatabasebetaFinite Group Databasebeta| order | 21412 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C53×C101 ⋊ C4 |
| Sylow | C101 ⋊ Dic53 |
| Sylow | C53 ⋊ #87938 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C53×C101 | C4 |
| prime radical, cosocle | C53×D101 | C2 |
| LCS | G ▷ C53×C101 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5353 |
Polycyclic presentation:
2^2,53,101|a^2=b,c^a=c^52,d^a=d^10,d^b=d^1001381 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21412, 11);