Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C61 ⋊ #2349 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator | C22×C61 | C23×C4 |
| Fitting | C2×C4×D4×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C2×C4×D4 | D61 |
| hypocenter | C61 | #2349 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
704 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,c^2=ef,b^a=be,c^a=cf,d^b=de,h^c=h^601250 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29698307, #29698308, #29698315, … |
| maximal normal subgroup of | #29698307, #29698308, #29698315, … |
| maximal quotient of | #29601442, #29601455, D4×#14519684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 7415);