Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C41 ⋊ C2 |
| Sylow | C41 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D41 |
| commutator, socle, cosocle | C2×C41 | C24 |
| Fitting | #41×C41 | C2 |
| hypercenter | #41 | D41 |
| hypocenter | C41 | H(5,𝔽2) |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^5,41|b^a=be,d^a=de,c^b=ce,f^c=f^40,f^d=f^40217 conjugacy classes — view the full character table.
| maximal subgroup of | #14580502, #14580505, #14580512, … |
| maximal normal subgroup of | #14580502, #14580505, #14580512, … |
| maximal quotient of | #14580808, #14580810, #14580816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 192);