Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | H(3,𝔽7) ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2×C7 | C7⋊D7 |
| commutator, hypocenter | H(3,𝔽7) | C4 |
| Fitting, prime radical, cosocle | C2×H(3,𝔽7) | C2 |
| LCS | G ▷ H(3,𝔽7) | |
| UCS | C1 ◁ C2×C7 | |
57 conjugacy classes of subgroups.
| transitive degree | μt(G) = 196 |
Polycyclic presentation:
2^2,7^3|a^2=b,c^a=c^6,d^a=d^6,d^c=de76 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1372, 10);