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AGL(1,𝔽5)×C29×C49 #43249253

order28420
automorphism?
homologyAbelianization (H1) = C4×C29×C49 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C29×C49

Splittings

Fitting, HallC5×C29×C49 ⋊ C4
derived, SylowC5 ⋊ C4×C29×C49
HallC5×C49 ⋊ C4×C29
HallC5×C29 ⋊ C4×C49

Subgroups

subgroupG/H
center, hypercenterC29×C49AGL(1,𝔽5)
commutator, hypocenterC5C4×C29×C49
FrattiniC7C7×AGL(1,𝔽5)×C29
FittingC5×C29×C49C4
socleC5×C7×C29C4×C7
prime radicalC7×D5×C29C2×C7
cosocleC7×D5C2×C7×C29
LCSG ▷ C5
UCSC1 ◁ C29×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7105

Conjugacy classes & character table

7105 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28420, 28);