Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #2985 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C61×#431 | C2 |
| hypercenter | #431 | D61 |
| hypocenter | C61 | #2985 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #431 | |
322 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 161 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,c^b=ce,d^b=dg,h^b=h^601244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29576606, #29576610, #29576620, … |
| maximal normal subgroup of | #29576606, #29576610, #29576620, … |
| maximal quotient of | #29678765, #29678785, #29679093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13604);