Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#14515349 |
| derived, Sylow | C241 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D241 |
| commutator, hypocenter | C241 | C22×C8 |
| Frattini | C4 | C22×D241 |
| Fitting | C22×C4×C241 | C2 |
| socle | C23×C241 | C4 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
1952 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29507471, #29507472, #29507479, … |
| maximal normal subgroup of | #29507471, #29507472, #29507479, … |
| maximal quotient of | C2×C4×#14515349, C2×C22⋊#14515349, C2×C4⋊#14515349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 148);