Finite Group DatabasebetaFinite Group Databasebeta| order | 7376 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic461 |
| derived, Sylow | C461 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D461 |
| commutator, hypocenter | C461 | C42 |
| Frattini | C22 | C2×D461 |
| Fitting | C2×C4×C461 | C2 |
| socle | C22×C461 | C22 |
| LCS | G ▷ C461 | |
| UCS | C1 ◁ C2×C4 | |
30 conjugacy classes of subgroups.
1856 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic461, #28414028, #28414044, … |
| maximal normal subgroup of | C8×Dic461, #28414028, #28414044, … |
| maximal quotient of | #28414025, C8×Dic461, C4×#16814779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7376, 16);