Finite Group DatabasebetaFinite Group Databasebeta| order | 1376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C43 ⋊ C2 |
| Sylow | C43 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D43 |
| commutator, socle, cosocle | C2×C43 | C24 |
| Fitting | C2×D4×C43 | C2 |
| hypercenter | C2×D4 | D43 |
| hypocenter | C43 | H(5,𝔽2) |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 344 |
Polycyclic presentation:
2^5,43|b^a=be,d^a=de,c^b=ce,f^d=f^42227 conjugacy classes — view the full character table.
| maximal subgroup of | #14583066, #14583069, #14583076, … |
| maximal normal subgroup of | #14583066, #14583069, #14583076, … |
| maximal quotient of | #14583371, #14583372, #14583374, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1376, 191);