Finite Group DatabasebetaFinite Group Databasebeta| order | 10100 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C101 · Schur multiplier (H2) = C1 |
| direct product | #1043×C101 |
| Fitting, socle, Hall | C52×C101 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | #1043 |
| commutator, hypocenter | C52 | C4×C101 |
| Frattini | C1 | G |
| Fitting, socle | C52×C101 | C4 |
| prime radical | C5⋊D5×C101 | C2 |
| cosocle | C5⋊D5 | C2×C101 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C101 | |
48 conjugacy classes of subgroups.
1010 conjugacy classes — view the full character table.
| maximal subgroup of | C101×#1043⋊C3, C3×#1043×C101, C101×C3⋊#1043 |
| maximal normal subgroup of | C101×#1043⋊C3, C3×#1043×C101 |
| maximal quotient of | C3×#1043×C101, C101×C3⋊#1043 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10100, 55);