Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #2984 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C2×C4×Q8×C61 | C2 |
| hypercenter | C2×C4×Q8 | D61 |
| hypocenter | C61 | #2984 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×Q8 | |
364 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,h^a=h^60,c^b=ceg1250 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29575841, #29575845, #29575855, … |
| maximal normal subgroup of | #29575841, #29575845, #29575855, … |
| maximal quotient of | #29678755, #29679077, #29679085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13599);