Finite Group DatabasebetaFinite Group Databasebeta| order | 7376 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic461 |
| Sylow | C461 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D461 |
| commutator | C2×C461 | C2×C4 |
| Fitting | C2×C4×C461 | C2 |
| socle | C22×C461 | C22 |
| hypercenter | C2×C4 | D461 |
| hypocenter | C461 | C4⋊C4 |
| LCS | G ▷ C2×C461 ▷ C461 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,461|a^2=d,b^2=c,b^a=bc,e^a=e^4601850 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28414039, #28414040, #28414042, … |
| maximal normal subgroup of | #28414039, #28414040, #28414042, … |
| maximal quotient of | #28414025, C4⋊#16814779, #28414050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7376, 20);