Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C241 ⋊ C4 |
| Sylow | C241 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#11757210 |
| commutator, socle | C2×C241 | C42 |
| Fitting | C8×C241 | C4 |
| hypercenter | C8 | #11757210 |
| hypocenter | C241 | #97 |
| LCS | G ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C4 ◁ C8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,241|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^177,f^d=f^240500 conjugacy classes — view the full character table.
| maximal subgroup of | #29508607, #29508608, C2×#21440696, … |
| maximal normal subgroup of | #29508607, #29508608, C2×#21440696, … |
| maximal quotient of | #29508558, #29508559, #29508582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 200);