Finite Group Databasebeta

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C5×C19⋊(Dic11⋊C5) #35229857

order20900
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C19⋊(Dic11⋊C5)
unambiguous semidirect productC19⋊(C5×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C5×Dic19)
unambiguous semidirect productDic209⋊C52
unambiguous semidirect product(C5×Dic209)⋊C5

Splittings

derived, HallC11×C19 ⋊ C4×C52
HallC5×C19×C11⋊C5 ⋊ C4
HallDic209 ⋊ C52
HallC5×C11⋊C5 ⋊ Dic19
SylowC19 ⋊ C5×Dic11⋊C5
SylowC11 ⋊ C52×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C5C19⋊AGL(1,𝔽11)
commutator, hypocenterC11×C19C4×C52
FrattiniC2C5×C19⋊AGL(1,𝔽11)
Fitting, socleC2×C5×C11×C19C2×C5
prime radicalC2×C5×C19×C11⋊C5C2
cosocleC2×C11×C19C2×C52
LCSG ▷ C11×C19
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4180

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 39);