Finite Group Databasebeta

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C2×C61×D7⋊C9 #29506729

order15372
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C22×C9×C61 · Schur multiplier (H2) = C2

Aliases

direct productC2×C61×D7⋊C9
unambiguous semidirect productD7⋊(C2×C9×C61)
unambiguous semidirect product(C2×D7)⋊(C9×C61)
unambiguous semidirect product(C7⋊C9)⋊(C22×C61)
unambiguous semidirect product(C2×C7⋊C9)⋊(C2×C61)

Splittings

derived, SylowC7 ⋊ C22×C9×C61
HallC61×C7⋊C9 ⋊ C22
HallC2×D7×C61 ⋊ C9
HallC7×C61 ⋊ C22×C9
HallC7⋊C9 ⋊ C22×C61
HallC2×D7 ⋊ C9×C61

Subgroups

subgroupG/H
center, hypercenterC2×C3×C61AGL(1,𝔽7)
commutator, hypocenterC7C22×C9×C61
FrattiniC3C2×AGL(1,𝔽7)×C61
Fitting, socleC2×C3×C7×C61C2×C3
prime radicalC2×C3×D7×C61C3
cosocleC3×C7C22×C3×C61
LCSG ▷ C7
UCSC1 ◁ C2×C3×C61

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7686

Conjugacy classes & character table

2562 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15372, 39);