Finite Group DatabasebetaFinite Group Databasebeta| order | 9824 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C307 ⋊ C2 |
| Sylow | C307 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D307 |
| commutator, socle, cosocle | C2×C307 | C24 |
| Fitting | #41×C307 | C2 |
| hypercenter | #41 | D307 |
| hypocenter | C307 | H(5,𝔽2) |
| LCS | G ▷ C2×C307 ▷ C307 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,307|b^a=be,d^a=de,c^b=ce,f^c=f^306,f^d=f^3061547 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34088053, #34088056, #34088063, … |
| maximal normal subgroup of | #34088053, #34088056, #34088063, … |
| maximal quotient of | #34088359, #34088361, #34088367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9824, 192);