Finite Group Databasebeta

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C2×C5×#14274255 #34062012

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

Aliases

direct productC2×C5×#14274255

Splittings

Fitting, HallC2×C5×C13×C49 ⋊ C3
derived, HallC13×C49 ⋊ C2×C3×C5
HallC5×C13×C49 ⋊ C2×C3
HallC2×C13×C49 ⋊ C3×C5
HallC2×C5×C49 ⋊ C13⋊C3
HallC5×C49 ⋊ C2×C13⋊C3
HallC2×C5×C13 ⋊ C49⋊C3
HallC2×C49 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C2×C49⋊C3
SylowC49 ⋊ C2×C5×C13⋊C3
HallC2×C13 ⋊ C5×C49⋊C3
SylowC13 ⋊ C2×C5×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#14274255
commutator, cosocle, hypocenterC13×C49C2×C3×C5
FrattiniC7C2×C5×#63271
FittingC2×C5×C13×C49C3
socleC2×C5×C7×C13ΓL(1,𝔽8)
LCSG ▷ C13×C49
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6370

Conjugacy classes & character table

2150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×#14274255, C5×#21439438, C5×#21439442, …
maximal normal subgroup ofC4×C5×#14274255, C5×#21439438, C5×#21439442, …
maximal quotient ofC4×C5×#14274255, C22×C5×#14274255

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 5);