Finite Group DatabasebetaFinite Group Databasebeta| order | 605 |
| isoclinism | isoclinic class of #10597243 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C112 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 121 |
Polycyclic presentation:
5,11^2|b^a=b^4,c^a=c^429 conjugacy classes — view the full character table.
| maximal subgroup of | #11925892, #11925895, C2×#10597243, … |
| maximal normal subgroup of | #11925892, #11925895, C2×#10597243, … |
| maximal quotient of | C2×#10597243, C3×#10597243, #15690027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(605, 4);