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C5×D13×C49⋊C3 #34062029

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

Aliases

direct productC5×D13×C49⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5D13×C49⋊C3
commutator, cosocle, hypocenterC13×C49C2×C3×C5
FrattiniC7C5×ΓL(1,𝔽8)×D13
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

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

Relationships

maximal subgroup ofC5×(C49⋊C3)⋊#261, C5×D13×D49⋊C3, C5×#261×C49⋊C3, …
maximal normal subgroup ofC5×(C49⋊C3)⋊#261, C5×D13×D49⋊C3, C5×#261×C49⋊C3, …
maximal quotient ofC5×Dic13×C49⋊C3, C2×C5×D13×C49⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 22);