Finite Group Databasebeta

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C5×#16838414 #34062031

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#16838414

Splittings

Fitting, HallC5×C13×C49 ⋊ C2×C3
derived, HallC13×C49 ⋊ C2×C3×C5
HallC5×#14274255 ⋊ C2
HallC5×D13×C49 ⋊ C3
Hall#14274255 ⋊ C2×C5
HallD13×C49 ⋊ C3×C5
HallC5×C49 ⋊ D13⋊C3
HallC5×D13 ⋊ C49⋊C3
HallC5×C13 ⋊ C2×C49⋊C3
SylowC49 ⋊ C5×D13⋊C3
HallD13 ⋊ C5×C49⋊C3
SylowC13 ⋊ C2×C5×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#16838414
commutator, cosocle, hypocenterC13×C49C2×C3×C5
FrattiniC7C5×#10587717
FittingC5×C13×C49C2×C3
socleC5×C7×C13C2×ΓL(1,𝔽8)
LCSG ▷ C13×C49
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#21439463, C5×#16838414⋊C2, C5×#21439460, …
maximal normal subgroup ofC5×#21439463, C5×#16838414⋊C2, C5×#21439460, …
maximal quotient ofC5×#21439438, C2×C5×#16838414

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 24);