Finite Group DatabasebetaFinite Group Databasebeta| order | 11540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C577 ⋊ C4 |
| Sylow | C577 ⋊ Dic5 |
| Sylow | C5 ⋊ #14556313 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C577 | C4 |
| prime radical, cosocle | C5×D577 | C2 |
| LCS | G ▷ C5×C577 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,577|a^2=b,c^a=c^4,d^a=d^553,d^b=d^576728 conjugacy classes — view the full character table.
| maximal subgroup of | #26040413⋊C3, C3×#26040413, C3⋊#26040413 |
| maximal normal subgroup of | #26040413⋊C3, C3×#26040413 |
| maximal quotient of | C3×#26040413, C3⋊#26040413 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11540, 11);