Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C353 ⋊ C2 |
| Sylow | C353 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D353 |
| commutator, socle, cosocle | C2×C353 | C24 |
| Fitting | #41×C353 | C2 |
| hypercenter | #41 | D353 |
| hypocenter | C353 | H(5,𝔽2) |
| LCS | G ▷ C2×C353 ▷ C353 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,353|b^a=be,d^a=de,c^b=ce,f^c=f^352,f^d=f^3521777 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36377953, #36377956, #36377963, … |
| maximal normal subgroup of | #36377953, #36377956, #36377963, … |
| maximal quotient of | #36378259, #36378261, #36378267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 192);