Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C241 ⋊ C2 |
| Sylow | C241 ⋊ #100 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16838747 |
| commutator | C22×C241 | C2×C4 |
| Frattini | C2×C4 | C2×D241 |
| Fitting | M16×C241 | C2 |
| socle | C2×C241 | C22⋊C4 |
| hypercenter | M16 | D241 |
| hypocenter | C241 | #100 |
| LCS | G ▷ C22×C241 ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ M16 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,241|a^2=d,d^2=e,b^a=bc,c^a=ce,d^b=de,f^b=f^2401211 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×D241, C2×#21440558, #29507699, … |
| maximal normal subgroup of | #100×D241, C2×#21440558, #29507699, … |
| maximal quotient of | #29507440, #29507456, #29507460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 62);