Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | M16×Dic122 |
| Sylow | C61 ⋊ Q8×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C4×M16×C61 | C2 |
| hypercenter | C4×M16 | D61 |
| hypocenter | C61 | Q8×M16 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
388 conjugacy classes of subgroups.
1250 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29574347, #29574351, #29574361, … |
| maximal normal subgroup of | #29574347, #29574351, #29574361, … |
| maximal quotient of | M16×C4⋊Dic61, M16×#11758196, #29678662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13463);