Finite Group Databasebeta

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C5×C29×Dic11⋊C5 #44542013

order31900
automorphism?
homologyAbelianization (H1) = C4×C52×C29 · Schur multiplier (H2) = C5

Aliases

direct productC5×C29×Dic11⋊C5
unambiguous semidirect productDic11⋊(C52×C29)
unambiguous semidirect product(C11⋊C5)⋊(C4×C5×C29)
unambiguous semidirect product(C5×Dic11)⋊(C5×C29)
unambiguous semidirect product(C29×Dic11)⋊C52
unambiguous semidirect product(C5×C29×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C4×C52×C29
HallC5×C29×C11⋊C5 ⋊ C4
HallC29×Dic11 ⋊ C52
HallC11×C29 ⋊ C4×C52
HallC5×C11⋊C5 ⋊ C4×C29
HallDic11 ⋊ C52×C29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C29AGL(1,𝔽11)
commutator, hypocenterC11C4×C52×C29
FrattiniC2C5×C29×AGL(1,𝔽11)
Fitting, socleC2×C5×C11×C29C2×C5
prime radicalC2×C5×C29×C11⋊C5C2
cosocleC2×C11C2×C52×C29
LCSG ▷ C11
UCSC1 ◁ C2×C5×C29

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6380

Conjugacy classes & character table

3190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31900, 48);