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C2×AGL(1,𝔽5)×C49 #14519937

order1960
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C4×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×AGL(1,𝔽5)×C49
unambiguous semidirect productD5⋊(C4×C49)

Splittings

FittingC2×C5×C49 ⋊ C4
derived, SylowC5 ⋊ C2×C4×C49
HallC5×C49 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC2×C49AGL(1,𝔽5)
commutator, hypocenterC5C2×C4×C49
FrattiniC7C2×C7×AGL(1,𝔽5)
FittingC2×C5×C49C4
socleC2×C5×C7C4×C7
prime radicalC2×C7×D5C2×C7
cosocleC7×D5C22×C7
LCSG ▷ C5
UCSC1 ◁ C2×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 490

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 34);