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C31×(C11⋊C5)⋊AGL(1,𝔽5) #46802069

order34100
automorphism?
homologyAbelianization (H1) = C4×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×(C11⋊C5)⋊AGL(1,𝔽5)
unambiguous semidirect product(C11⋊C5)⋊(AGL(1,𝔽5)×C31)
unambiguous semidirect product(C11⋊AGL(1,𝔽5))⋊(C5×C31)

Splittings

Fitting, socleC5×C11×C31 ⋊ C4×C5
derivedC5×C11 ⋊ C4×C5×C31
HallC5×C31×C11⋊C5 ⋊ C4
HallC11×C31 ⋊ C5×AGL(1,𝔽5)
HallC5×C11⋊C5 ⋊ C4×C31
SylowC11 ⋊ C5×AGL(1,𝔽5)×C31

Subgroups

subgroupG/H
center, hypercenterC31(C11⋊C5)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C5×C31
FrattiniC1G
Fitting, socleC5×C11×C31C4×C5
prime radicalD5×C31×C11⋊C5C2
cosocleD5×C11C2×C5×C31
LCSG ▷ C5×C11
UCSC1 ◁ C31

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1705

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 160);