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C7×D1245 #31775235

order17430
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D1245
unambiguous semidirect productC3⋊(C7×D415)
unambiguous semidirect productC5⋊(C7×D249)
unambiguous semidirect productC83⋊(C7×D15)

Splittings

Fitting, socle, HallC3×C5×C7×C83 ⋊ C2
derived, HallC3×C5×C83 ⋊ C2×C7
HallC5×C7×C83 ⋊ D3
HallC3×C7×C83 ⋊ D5
HallC7×C83 ⋊ D15
HallC5×C83 ⋊ D3×C7
HallC3×C83 ⋊ C7×D5
HallC3×C5×C7 ⋊ D83
SylowC83 ⋊ C7×D15
HallC5×C7 ⋊ D249
HallC3×C7 ⋊ D415
HallC3×C5 ⋊ C7×D83
SylowC5 ⋊ C7×D249
SylowC3 ⋊ C7×D415

Subgroups

subgroupG/H
center, hypercenterC7D1245
commutator, cosocle, hypocenterC3×C5×C83C2×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C83C2
LCSG ▷ C3×C5×C83
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8715

Conjugacy classes & character table

4368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D15×D83, D7×D1245, D581⋊D15, …
maximal normal subgroup ofC7×D15×D83, D7×D1245, D581⋊D15, …
maximal quotient ofC7×Dic1245, C2×C7×D1245

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17430, 15);