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C2×AGL(1,𝔽7)×C97⋊C3 #37567867

order24444
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×AGL(1,𝔽7)×C97⋊C3
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C97⋊C3)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C97⋊C3)
unambiguous semidirect product(C2×AGL(1,𝔽7)×C97)⋊C3
unambiguous semidirect product(C2×#16861353)⋊C3
unambiguous semidirect product(C2×#16861354)⋊C3
unambiguous semidirect product(C2×D7×C97⋊C3)⋊C3

Splittings

Fitting, socleC2×C7×C97 ⋊ C2×C32
derived, HallC7×C97 ⋊ C22×C32
HallΓL(1,𝔽8)×C97⋊C3 ⋊ C22
HallC2×D7×C97 ⋊ C32
SylowC97 ⋊ C2×C3×AGL(1,𝔽7)
HallC2×D7 ⋊ C3×C97⋊C3
SylowC7 ⋊ C22×C3×C97⋊C3

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽7)×C97⋊C3
commutator, cosocle, hypocenterC7×C97C22×C32
FrattiniC1G
Fitting, socleC2×C7×C97C2×C32
LCSG ▷ C7×C97
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1358

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24444, 130);