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C2×ΓL(1,𝔽8)⋊(D11⋊C25) #37528228

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

Aliases

direct productC2×ΓL(1,𝔽8)⋊(D11⋊C25)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(D11⋊C25)
unambiguous semidirect product(C2×C11⋊C25)⋊AGL(1,𝔽7)
unambiguous semidirect product(C2×C11⋊AGL(1,𝔽7))⋊C25
unambiguous semidirect product(C2×C7⋊(D11⋊C25))⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C22×C3×C25
FrattiniC5C2×ΓL(1,𝔽8)⋊AGL(1,𝔽11)
Fitting, socleC2×C5×C7×C11C2×C3×C5
prime radicalC2×C5×C11⋊AGL(1,𝔽7)C5
cosocleC5×C7×C11C22×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3850

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 39);