Finite Group DatabasebetaFinite Group Databasebeta| order | 7376 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C461 ⋊ C2 |
| Sylow | C461 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D461 |
| commutator | C4×C461 | C22 |
| Frattini | C4 | C2×D461 |
| Fitting | Q8×C461 | C2 |
| socle | C2×C461 | D4 |
| hypercenter | Q8 | D461 |
| hypocenter | C461 | SD16 |
| LCS | G ▷ C4×C461 ▷ C2×C461 ▷ C461 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,461|a^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^4601157 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D461, C2×#20301488, #28414138, … |
| maximal normal subgroup of | SD16×D461, C2×#20301488, #28414138, … |
| maximal quotient of | #28414038, #28414042, #28414049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7376, 27);