Finite Group DatabasebetaFinite Group Databasebeta| order | 8692 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C41×C53 ⋊ C4 |
| Sylow | C53 ⋊ #4223 |
| Sylow | C41 ⋊ Dic53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C41×C53 | C4 |
| LCS | G ▷ C41×C53 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,41,53|a^2=b,c^a=c^32,d^a=d^52,c^b=c^40586 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#22576331, C3⋊#22576331 |
| maximal normal subgroup of | C3×#22576331 |
| maximal quotient of | C3×#22576331, C3⋊#22576331 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8692, 10);