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C59×Dic7⋊C9 #28415482

order14868
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C4×C9×C59 · Schur multiplier (H2) = C1

Aliases

direct productC59×Dic7⋊C9
unambiguous semidirect productDic7⋊(C9×C59)
unambiguous semidirect product(C7⋊C9)⋊(C4×C59)
unambiguous semidirect product(Dic7×C59)⋊C9

Splittings

derived, SylowC7 ⋊ C4×C9×C59
HallC59×C7⋊C9 ⋊ C4
HallDic7×C59 ⋊ C9
HallC7×C59 ⋊ C4×C9
HallC7⋊C9 ⋊ C4×C59
HallDic7 ⋊ C9×C59

Subgroups

subgroupG/H
center, hypercenterC2×C3×C59AGL(1,𝔽7)
commutator, hypocenterC7C4×C9×C59
FrattiniC2×C3AGL(1,𝔽7)×C59
Fitting, socle, prime radicalC2×C3×C7×C59C2×C3
cosocleC2×C3×C7C2×C3×C59
LCSG ▷ C7
UCSC1 ◁ C2×C3×C59

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14868

Conjugacy classes & character table

2478 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14868, 11);