Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C241 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D241 |
| commutator, socle | C2×C241 | C22×C4 |
| Fitting | #41×C241 | C2 |
| hypercenter | #41 | D241 |
| hypocenter | C241 | #131 |
| LCS | G ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,241|a^2=d,d^2=e,f^a=f^240,c^b=ce1220 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29507831, #29507834, #29507836, … |
| maximal normal subgroup of | #29507831, #29507834, #29507836, … |
| maximal quotient of | #29507673, #29507684, #29507744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 153);