Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3498 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | C2×H(5,𝔽2)×C83 | C2 |
| hypercenter | C2×H(5,𝔽2) | D83 |
| hypocenter | C83 | #3498 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
1748 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|c^2=g,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^821438 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319984, #35413588, #35413590, … |
| maximal normal subgroup of | #35319984, #35413588, #35413590, … |
| maximal quotient of | #35564504, #35564775, #35564805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18284);