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C2×C25×C11⋊AGL(1,𝔽7) #37528260

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

Aliases

direct productC2×C25×C11⋊AGL(1,𝔽7)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(D11×C25)
unambiguous semidirect product(C2×C25×D77)⋊C3

Splittings

FittingC2×C7×C11×C25 ⋊ C2×C3
derived, HallC7×C11 ⋊ C22×C3×C25
HallC2×C25×D77 ⋊ C3
HallC11×ΓL(1,𝔽8)×C25 ⋊ C22
HallC7×C11×C25 ⋊ C22×C3
HallΓL(1,𝔽8)×C25 ⋊ C2×D11
HallC2×D77 ⋊ C3×C25
HallC11×C25 ⋊ C2×AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ C22×C25
HallC7×C25 ⋊ C2×C3×D11
HallΓL(1,𝔽8) ⋊ C2×D11×C25
SylowC11 ⋊ C2×C25×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×D11×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C22×C3×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×C7×C11C22×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3850

Conjugacy classes & character table

1600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 71);