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C7×D2405 #46797608

order33670
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D2405
unambiguous semidirect productC5⋊(C7×D481)
unambiguous semidirect productC13⋊(C7×D185)
unambiguous semidirect productC37⋊(C7×D65)

Splittings

Fitting, socle, HallC5×C7×C13×C37 ⋊ C2
derived, HallC5×C13×C37 ⋊ C2×C7
HallC7×C13×C37 ⋊ D5
HallC5×C7×C37 ⋊ D13
HallC13×C37 ⋊ C7×D5
HallC5×C7×C13 ⋊ D37
HallC7×C37 ⋊ D65
HallC5×C37 ⋊ C7×D13
HallC7×C13 ⋊ D185
HallC5×C13 ⋊ C7×D37
SylowC37 ⋊ C7×D65
HallC5×C7 ⋊ D481
SylowC13 ⋊ C7×D185
SylowC5 ⋊ C7×D481

Subgroups

subgroupG/H
center, hypercenterC7D2405
commutator, cosocle, hypocenterC5×C13×C37C2×C7
FrattiniC1G
Fitting, socleC5×C7×C13×C37C2
LCSG ▷ C5×C13×C37
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16835

Conjugacy classes & character table

8428 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33670, 12);