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D3×AGL(1,𝔽7)×C97 #37567889

order24444
automorphism?
homologyAbelianization (H1) = C22×C3×C97 · Schur multiplier (H2) = C2

Aliases

direct productD3×AGL(1,𝔽7)×C97
unambiguous semidirect productD7⋊(C3×D3×C97)
unambiguous semidirect product(D3×D7)⋊(C3×C97)
unambiguous semidirect product(C3×AGL(1,𝔽7))⋊(C2×C97)
unambiguous semidirect product(D3×ΓL(1,𝔽8))⋊(C2×C97)
unambiguous semidirect product(C3⋊AGL(1,𝔽7))⋊(C2×C97)

Splittings

Fitting, socleC3×C7×C97 ⋊ C22×C3
derivedC3×C7 ⋊ C22×C3×C97
HallC3×ΓL(1,𝔽8)×C97 ⋊ C22
HallC7×C97 ⋊ C2×C3×D3
HallC3×ΓL(1,𝔽8) ⋊ C22×C97
SylowC7 ⋊ C2×C3×D3×C97

Subgroups

subgroupG/H
center, hypercenterC97D3×AGL(1,𝔽7)
commutator, cosocle, hypocenterC3×C7C22×C3×C97
FrattiniC1G
Fitting, socleC3×C7×C97C22×C3
LCSG ▷ C3×C7
UCSC1 ◁ C97

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2037

Conjugacy classes & character table

2037 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24444, 152);