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C2×D5×#13046196 #38785151

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

Aliases

direct productC2×D5×#13046196
unambiguous semidirect productC5⋊(C22×#13046196)
unambiguous semidirect product(C2×C5)⋊(C2×#13046196)

Splittings

Fitting, socleC2×C5×C7×C61 ⋊ C2×C3
derived, HallC5×C7×C61 ⋊ C22×C3
HallC2×C7×D5×C61 ⋊ C3
HallC5×#13046196 ⋊ C22
HallC2×D5×C61 ⋊ ΓL(1,𝔽8)
HallC7×C61 ⋊ C2×C3×D5
HallC5×C61 ⋊ C22×ΓL(1,𝔽8)
HallC2×C7×D5 ⋊ C61⋊C3
SylowC61 ⋊ C2×D5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C22×C61⋊C3
SylowC7 ⋊ C2×D5×C61⋊C3
SylowC5 ⋊ C22×#13046196

Subgroups

subgroupG/H
center, hypercenterC2D5×#13046196
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

1160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25620, 224);