Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
No aliases for this group.
| derived, Hall | C72×C61 ⋊ C3×C4 |
| Hall | C61×C7⋊Dic7 ⋊ C3 |
| Hall | C61⋊#3862 ⋊ C4 |
| Hall | C7⋊Dic7 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ #10596875 |
| Sylow | C72 ⋊ C4×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #31822446 |
| commutator, hypocenter | C72×C61 | C3×C4 |
| Fitting, socle, cosocle | C2×C72×C61 | C2×C3 |
| prime radical | C2×C61⋊#3862 | C2 |
| LCS | G ▷ C72×C61 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5124 |
Polycyclic presentation:
2,3,7^2,61,2|a^2=f,c^a=c^6,d^a=d^6,c^b=c^2,d^b=d^4,e^b=e^131068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 98);