Finite Group DatabasebetaFinite Group Databasebeta| order | 7312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C457 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14270052 |
| commutator, socle | C2×C457 | C2×C4 |
| Fitting | C4×C457 | C4 |
| hypercenter | C4 | #14270052 |
| hypocenter | C457 | M16 |
| LCS | G ▷ C2×C457 ▷ C457 | |
| UCS | C1 ◁ C2 ◁ C4 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,457|a^2=c,c^2=d,b^a=bd,e^a=e^348,e^b=e^456,e^c=e^456466 conjugacy classes — view the full character table.
| maximal subgroup of | #28410616, #28410617, #28410622, … |
| maximal normal subgroup of | #28410616, #28410617, #28410622, … |
| maximal quotient of | #28410607, #28410609, C4⋊#16814539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7312, 50);