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C59×D273 #44567265

order32214
automorphism?
homologyAbelianization (H1) = C2×C59 · Schur multiplier (H2) = C1

Aliases

direct productC59×D273
unambiguous semidirect productC3⋊(C59×D91)
unambiguous semidirect productC7⋊(C59×D39)
unambiguous semidirect productC13⋊(D21×C59)

Splittings

Fitting, socle, HallC3×C7×C13×C59 ⋊ C2
derived, HallC3×C7×C13 ⋊ C2×C59
HallC7×C13×C59 ⋊ D3
HallC3×C13×C59 ⋊ D7
HallC3×C7×C59 ⋊ D13
HallC13×C59 ⋊ D21
HallC7×C59 ⋊ D39
HallC3×C59 ⋊ D91
HallC7×C13 ⋊ D3×C59
HallC3×C13 ⋊ D7×C59
HallC3×C7 ⋊ D13×C59
SylowC13 ⋊ D21×C59
SylowC7 ⋊ C59×D39
SylowC3 ⋊ C59×D91

Subgroups

subgroupG/H
center, hypercenterC59D273
commutator, cosocle, hypocenterC3×C7×C13C2×C59
FrattiniC1G
Fitting, socleC3×C7×C13×C59C2
LCSG ▷ C3×C7×C13
UCSC1 ◁ C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16107

Conjugacy classes & character table

8142 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32214, 19);