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C17×C3⋊D105 #24924228

order10710
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C3

Aliases

direct productC17×C3⋊D105
unambiguous semidirect productC3⋊(C17×D105)
unambiguous semidirect productC5⋊(C17×C3⋊D21)
unambiguous semidirect productC7⋊(C17×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derived, HallC32×C5×C7 ⋊ C2×C17
HallC32×C7×C17 ⋊ D5
HallC32×C5×C17 ⋊ D7
HallC5×C7×C17 ⋊ C3⋊D3
HallC32×C17 ⋊ D35
HallC7×C17 ⋊ C3⋊D15
HallC5×C17 ⋊ C3⋊D21
HallC32×C7 ⋊ D5×C17
HallC32×C5 ⋊ D7×C17
HallC5×C7 ⋊ C17×C3⋊D3
SylowC32 ⋊ C17×D35
SylowC7 ⋊ C17×C3⋊D15
SylowC5 ⋊ C17×C3⋊D21

Subgroups

subgroupG/H
center, hypercenterC17C3⋊D105
commutator, cosocle, hypocenterC32×C5×C7C2×C17
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C32×C5×C7
UCSC1 ◁ C17

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2703 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C17×D105, D51⋊D105, C17×D15×D21, …
maximal normal subgroup ofD3×C17×D105, D51⋊D105, C17×D15×D21, …
maximal quotient ofC17×C3⋊Dic105, C2×C17×C3⋊D105

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 43);