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C2×C5⋊(ΓL(1,𝔽8)⋊D61) #38785147

order25620
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(ΓL(1,𝔽8)⋊D61)
unambiguous semidirect product(C2×C5)⋊(ΓL(1,𝔽8)⋊D61)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊D305

Splittings

Fitting, socleC2×C5×C7×C61 ⋊ C2×C3
derived, HallC5×C7×C61 ⋊ C22×C3
HallC2×D2135 ⋊ C3
HallC5×ΓL(1,𝔽8)×C61 ⋊ C22
HallΓL(1,𝔽8)×C61 ⋊ C2×D5
HallC7×C61 ⋊ C2×C3×D5
HallC5×C61 ⋊ C2×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×D61
SylowC61 ⋊ C2×C5⋊AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D61
HallΓL(1,𝔽8) ⋊ C2×D305
SylowC7 ⋊ C2×C3×D305
SylowC5 ⋊ C2×ΓL(1,𝔽8)⋊D61

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(ΓL(1,𝔽8)⋊D61)
commutator, cosocle, hypocenterC5×C7×C61C22×C3
FrattiniC1G
Fitting, socleC2×C5×C7×C61C2×C3
LCSG ▷ C5×C7×C61
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4270

Conjugacy classes & character table

1534 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25620, 220);