Finite Group DatabasebetaFinite Group Databasebeta| order | 8992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C281 ⋊ C2 |
| Sylow | C281 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D281 |
| commutator, socle | C2×C281 | C24 |
| Fitting | #41×C281 | C2 |
| hypercenter | #41 | D281 |
| hypocenter | C281 | H(5,𝔽2) |
| LCS | G ▷ C2×C281 ▷ C281 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,281|b^a=be,d^a=de,c^b=ce,f^c=f^280,f^d=f^2801417 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31823629, #31823632, #31823639, … |
| maximal normal subgroup of | #31823629, #31823632, #31823639, … |
| maximal quotient of | #31823935, #31823937, #31823943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8992, 192);