Finite Group DatabasebetaFinite Group Databasebeta| order | 11005 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C71 ⋊ C5 |
| Sylow | C71 ⋊ ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C71 | C5 |
| LCS | G ▷ C31×C71 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
5,31,71|b^a=b^8,c^a=c^5445 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#24927023, #36347352, #36347358, … |
| maximal normal subgroup of | C2×#24927023, #36347352, #36347358, … |
| maximal quotient of | C2×#24927023, C3×#24927023 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11005, 5);