Finite Group DatabasebetaFinite Group Databasebeta| order | 37698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C61×C103 ⋊ C2×C3 |
| Hall | #34038115 ⋊ C2 |
| Hall | C61×D103 ⋊ C3 |
| Hall | D103 ⋊ C61⋊C3 |
| Sylow | C103 ⋊ C2×C61⋊C3 |
| Sylow | C61 ⋊ D103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C61×C103 | C2×C3 |
| LCS | G ▷ C61×C103 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6283 |
Polycyclic presentation:
2,3,61,103|d^a=d^102,c^b=c^47,d^b=d^461083 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37698, 16);