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C29×(C11⋊C5)⋊AGL(1,𝔽5) #44542036

order31900
automorphism?
homologyAbelianization (H1) = C4×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×(C11⋊C5)⋊AGL(1,𝔽5)
unambiguous semidirect product(C11⋊C5)⋊(AGL(1,𝔽5)×C29)
unambiguous semidirect product(C11⋊AGL(1,𝔽5))⋊(C5×C29)
unambiguous semidirect product(C29×C11⋊AGL(1,𝔽5))⋊C5

Splittings

Fitting, socleC5×C11×C29 ⋊ C4×C5
derivedC5×C11 ⋊ C4×C5×C29
HallC5×C29×C11⋊C5 ⋊ C4
HallC11×C29 ⋊ C5×AGL(1,𝔽5)
HallC5×C11⋊C5 ⋊ C4×C29
SylowC11 ⋊ C5×AGL(1,𝔽5)×C29

Subgroups

subgroupG/H
center, hypercenterC29(C11⋊C5)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C5×C29
FrattiniC1G
Fitting, socleC5×C11×C29C4×C5
prime radicalD5×C29×C11⋊C5C2
cosocleD5×C11C2×C5×C29
LCSG ▷ C5×C11
UCSC1 ◁ C29

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1595

Conjugacy classes & character table

841 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31900, 71);