Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C241 ⋊ C2 |
| Sylow | C241 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D241 |
| commutator, socle | C2×C241 | C24 |
| Fitting | #41×C241 | C2 |
| hypercenter | #41 | D241 |
| hypocenter | C241 | 2−1+4 |
| LCS | G ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C2 ◁ #41 | |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,241|b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,f^d=f^2401217 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29507888, #29507891, #29507898, … |
| maximal normal subgroup of | #29507888, #29507891, #29507898, … |
| maximal quotient of | #29508193, #29508194, #29508196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 193);