Finite Group DatabasebetaFinite Group Databasebeta| order | 7376 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C461 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14270406 |
| commutator, socle | C2×C461 | C2×C4 |
| Fitting | C4×C461 | C4 |
| hypercenter | C4 | #14270406 |
| hypocenter | C461 | M16 |
| LCS | G ▷ C2×C461 ▷ C461 | |
| UCS | C1 ◁ C2 ◁ C4 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,461|a^2=c,c^2=d,b^a=bd,e^a=e^48,e^b=e^460,e^c=e^460470 conjugacy classes — view the full character table.
| maximal subgroup of | #28414182, #28414183, #28414188, … |
| maximal normal subgroup of | #28414182, #28414183, #28414188, … |
| maximal quotient of | #28414173, #28414175, C4⋊#16814786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7376, 50);