Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C61 ⋊ #3407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#6923 |
| commutator, socle | C2×C61 | C23×C8 |
| Fitting | C2×#41×C61 | C4 |
| hypercenter | C2×#41 | #6923 |
| hypocenter | C61 | #3407 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
360 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,e^2=f,f^2=g,d^a=dg,h^a=h^11,c^b=cg,h^e=h^60368 conjugacy classes — view the full character table.
| maximal subgroup of | #30606491, #30606492, #30607379, … |
| maximal normal subgroup of | #30606491, #30606492, #30607379, … |
| maximal quotient of | #30623823, #30623833, #30623867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21477);