Finite Group Databasebeta

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C5×C19×Dic11⋊C5 #35229856

order20900
automorphism?
homologyAbelianization (H1) = C4×C52×C19 · Schur multiplier (H2) = C5

Aliases

direct productC5×C19×Dic11⋊C5
unambiguous semidirect productDic11⋊(C52×C19)
unambiguous semidirect product(C11⋊C5)⋊(C4×C5×C19)
unambiguous semidirect product(C5×Dic11)⋊(C5×C19)
unambiguous semidirect product(C19×Dic11)⋊C52
unambiguous semidirect product(C5×C19×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C4×C52×C19
HallC5×C19×C11⋊C5 ⋊ C4
HallC19×Dic11 ⋊ C52
HallC5×C11⋊C5 ⋊ C4×C19
HallC11×C19 ⋊ C4×C52
HallDic11 ⋊ C52×C19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C19AGL(1,𝔽11)
commutator, hypocenterC11C4×C52×C19
FrattiniC2C5×C19×AGL(1,𝔽11)
Fitting, socleC2×C5×C11×C19C2×C5
prime radicalC2×C5×C19×C11⋊C5C2
cosocleC2×C11C2×C52×C19
LCSG ▷ C11
UCSC1 ◁ C2×C5×C19

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4180

Conjugacy classes & character table

2090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 38);