Finite Group Databasebeta

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C13×C5⋊(D19⋊C3) #20301830

order7410
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C5⋊(D19⋊C3)
unambiguous semidirect productC5⋊(C13×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(D5×C13)
unambiguous semidirect productD95⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C13×C19 ⋊ C2×C3
derived, HallC5×C19 ⋊ C2×C3×C13
HallC5×C13×C19⋊C3 ⋊ C2
HallC13×D95 ⋊ C3
HallC13×C19⋊C3 ⋊ D5
HallC5×C19⋊C3 ⋊ C2×C13
HallC13×C19 ⋊ C3×D5
HallD95 ⋊ C3×C13
HallC5×C13 ⋊ D19⋊C3
HallC19⋊C3 ⋊ D5×C13
SylowC19 ⋊ C3×D5×C13
SylowC5 ⋊ C13×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC13C5⋊(D19⋊C3)
commutator, hypocenterC5×C19C2×C3×C13
FrattiniC1G
Fitting, socleC5×C13×C19C2×C3
LCSG ▷ C5×C19
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

351 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C13×D19⋊C3, D13×C5⋊(D19⋊C3), (C5⋊(D19⋊C3))⋊D13, …
maximal normal subgroup ofD5×C13×D19⋊C3, D13×C5⋊(D19⋊C3), (C5⋊(D19⋊C3))⋊D13, …
maximal quotient ofC13×(C19⋊C3)⋊Dic5, C2×C13×C5⋊(D19⋊C3), C13×C5⋊(#4294⋊C2), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7410, 37);