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C83×D105 #31775236

order17430
isoclinismisoclinic class of D105
automorphism?
homologyAbelianization (H1) = C2×C83 · Schur multiplier (H2) = C1

Aliases

direct productC83×D105
unambiguous semidirect productC3⋊(D35×C83)
unambiguous semidirect productC5⋊(D21×C83)
unambiguous semidirect productC7⋊(D15×C83)

Splittings

Fitting, socle, HallC3×C5×C7×C83 ⋊ C2
derived, HallC3×C5×C7 ⋊ C2×C83
HallC5×C7×C83 ⋊ D3
HallC3×C7×C83 ⋊ D5
HallC3×C5×C83 ⋊ D7
HallC7×C83 ⋊ D15
HallC5×C83 ⋊ D21
HallC3×C83 ⋊ D35
HallC5×C7 ⋊ D3×C83
HallC3×C7 ⋊ D5×C83
HallC3×C5 ⋊ D7×C83
SylowC7 ⋊ D15×C83
SylowC5 ⋊ D21×C83
SylowC3 ⋊ D35×C83

Subgroups

subgroupG/H
center, hypercenterC83D105
commutator, cosocle, hypocenterC3×C5×C7C2×C83
FrattiniC1G
Fitting, socleC3×C5×C7×C83C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C83

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8715

Conjugacy classes & character table

4482 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD83×D105, D7×D15×C83, D581⋊D15, …
maximal normal subgroup ofD83×D105, D7×D15×C83, D581⋊D15, …
maximal quotient ofC83×Dic105, C2×C83×D105

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17430, 16);