Finite Group Databasebeta

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C19×Dic5×C11⋊C5 #35229861

order20900
automorphism?
homologyAbelianization (H1) = C4×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×Dic5×C11⋊C5
unambiguous semidirect product(C11×Dic5)⋊(C5×C19)
unambiguous semidirect product(C11×C19×Dic5)⋊C5

Splittings

derivedC5×C11 ⋊ C4×C5×C19
HallC5×C19×C11⋊C5 ⋊ C4
HallC5×C11⋊C5 ⋊ C4×C19
HallC11×C19 ⋊ C5×Dic5
SylowC11 ⋊ C5×C19×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C19D5×C11⋊C5
commutator, hypocenterC5×C11C4×C5×C19
FrattiniC2D5×C19×C11⋊C5
Fitting, socleC2×C5×C11×C19C2×C5
prime radicalC2×C5×C19×C11⋊C5C2
cosocleC2×C5×C11C2×C5×C19
LCSG ▷ C5×C11
UCSC1 ◁ C2×C19

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4180

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 43);