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D65×#3861 #34062161

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

Aliases

direct productD65×#3861
unambiguous semidirect productC5⋊(D13×#3861)

Splittings

Fitting, socle, derived, HallC5×C72×C13 ⋊ C2×C3
HallC5×C13×#3861 ⋊ C2
HallC72×D65 ⋊ C3
HallC13×#3861 ⋊ D5
HallC5×#3861 ⋊ D13
HallC72×C13 ⋊ C3×D5
HallC5×C72 ⋊ C3×D13
HallC5×C13 ⋊ C2×#3861
SylowC72 ⋊ C3×D65
SylowC13 ⋊ D5×#3861
SylowC5 ⋊ D13×#3861

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

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

Relationships

maximal subgroup of#3861×#63122, #3861×#63121, #50303907, …
maximal normal subgroup of#3861×#63122, #3861×#63121, #50303907, …
maximal quotient of#3861×Dic65, C2×D65×#3861

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 154);