Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C61×#396 ⋊ C2 |
| Sylow | C61 ⋊ #2800 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator, socle | C23×C61 | C24 |
| Fitting | C61×#396 | C2 |
| hypercenter | #396 | D61 |
| hypocenter | C61 | #2800 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #396 | |
420 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=fg,b^2=e,c^2=eg,d^2=f,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^d=h^60692 conjugacy classes — view the full character table.
| maximal subgroup of | #29887946, #29887958, #29888020, … |
| maximal normal subgroup of | #29887946, #29887958, #29888020, … |
| maximal quotient of | #29608347, #29608374, #29608471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 12399);