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C2×C11×C25×AGL(1,𝔽7) #37528259

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C25×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C2×C3×C11×C25)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C11×C25)
unambiguous semidirect product(C2×D7)⋊(C3×C11×C25)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C11×C25)
unambiguous semidirect product(C2×D7×C25)⋊(C3×C11)
unambiguous semidirect product(C2×C11×D7×C25)⋊C3

Splittings

FittingC2×C7×C11×C25 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C11×C25
HallC2×C11×D7×C25 ⋊ C3
HallC11×ΓL(1,𝔽8)×C25 ⋊ C22
HallC7×C11×C25 ⋊ C22×C3
HallC2×D7×C25 ⋊ C3×C11
HallΓL(1,𝔽8)×C25 ⋊ C22×C11
HallC2×C11×D7 ⋊ C3×C25
HallC11×ΓL(1,𝔽8) ⋊ C22×C25
HallC7×C25 ⋊ C22×C3×C11
HallC7×C11 ⋊ C22×C3×C25
HallC2×D7 ⋊ C3×C11×C25
HallΓL(1,𝔽8) ⋊ C22×C11×C25

Subgroups

subgroupG/H
center, hypercenterC2×C11×C25AGL(1,𝔽7)
commutator, hypocenterC7C22×C3×C11×C25
FrattiniC5C2×C5×C11×AGL(1,𝔽7)
FittingC2×C7×C11×C25C2×C3
socleC2×C5×C7×C11C2×C3×C5
prime radicalC2×C5×C11×AGL(1,𝔽7)C5
cosocleC5×C7C22×C3×C5×C11
LCSG ▷ C7
UCSC1 ◁ C2×C11×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3850

Conjugacy classes & character table

3850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 70);