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C5×(C49⋊C3)⋊D13 #34062037

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

Aliases

direct productC5×(C49⋊C3)⋊D13
unambiguous semidirect product(C49⋊C3)⋊(C5×D13)

Splittings

Fitting, HallC5×C13×C49 ⋊ C2×C3
derived, HallC13×C49 ⋊ C2×C3×C5
HallC5×C13×C49⋊C3 ⋊ C2
HallC5×D637 ⋊ C3
HallC13×C49⋊C3 ⋊ C2×C5
HallD637 ⋊ C3×C5
HallC5×C49⋊C3 ⋊ D13
HallC5×C49 ⋊ C3×D13
HallC49⋊C3 ⋊ C5×D13
HallC5×C13 ⋊ D49⋊C3
SylowC49 ⋊ C3×C5×D13
SylowC13 ⋊ C5×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC5(C49⋊C3)⋊D13
commutator, cosocle, hypocenterC13×C49C2×C3×C5
FrattiniC7C5×ΓL(1,𝔽8)⋊D13
FittingC5×C13×C49C2×C3
socleC5×C7×C13AGL(1,𝔽7)
LCSG ▷ C13×C49
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D13×D49⋊C3, D5×(C49⋊C3)⋊D13, (C5⋊(D49⋊C3))⋊D13, …
maximal normal subgroup ofC5×D13×D49⋊C3, D5×(C49⋊C3)⋊D13, (C5⋊(D49⋊C3))⋊D13, …
maximal quotient ofC5×(C49⋊C3)⋊Dic13, C2×C5×(C49⋊C3)⋊D13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 30);