Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C61 ⋊ #2365 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator | C22×C61 | C23×C4 |
| Fitting | C2×C4×Q8×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C2×C4×Q8 | D61 |
| hypocenter | C61 | #2365 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
552 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,b^2=g,c^2=f,d^2=e,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 | #29702263, #29702265, #29702285, … |
| maximal normal subgroup of | #29702263, #29702265, #29702285, … |
| maximal quotient of | C4⋊C4×#11758196, #29601551, #29601554, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 7564);