Finite Group Databasebeta

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C29×(C11⋊C5)⋊Dic5 #44542016

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

Aliases

direct productC29×(C11⋊C5)⋊Dic5
unambiguous semidirect product(C11⋊C5)⋊(Dic5×C29)
unambiguous semidirect productDic55⋊(C5×C29)
unambiguous semidirect product(C29×Dic55)⋊C5

Splittings

derivedC5×C11 ⋊ C4×C5×C29
HallC5×C29×C11⋊C5 ⋊ C4
HallC11×C29 ⋊ C5×Dic5
HallC5×C11⋊C5 ⋊ C4×C29
SylowC11 ⋊ C5×Dic5×C29

Subgroups

subgroupG/H
center, hypercenterC2×C29C5⋊AGL(1,𝔽11)
commutator, hypocenterC5×C11C4×C5×C29
FrattiniC2C29×C5⋊AGL(1,𝔽11)
Fitting, socleC2×C5×C11×C29C2×C5
prime radicalC2×C5×C29×C11⋊C5C2
cosocleC2×C5×C11C2×C5×C29
LCSG ▷ C5×C11
UCSC1 ◁ C2×C29

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6380

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31900, 51);