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C13×AGL(1,𝔽5)×C37⋊C3 #43274176

order28860
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×AGL(1,𝔽5)×C37⋊C3
unambiguous semidirect product(AGL(1,𝔽5)×C37)⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C13×C37 ⋊ C3×C4
derived, HallC5×C37 ⋊ C3×C4×C13
HallC13×AGL(1,𝔽5)×C37 ⋊ C3
HallC5×C13×C37⋊C3 ⋊ C4
HallAGL(1,𝔽5)×C37 ⋊ C3×C13
HallC5×C37⋊C3 ⋊ C4×C13
HallC13×C37 ⋊ C3×AGL(1,𝔽5)
HallC5×C13 ⋊ C4×C37⋊C3
SylowC37 ⋊ C3×C13×AGL(1,𝔽5)
SylowC5 ⋊ C4×C13×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC13AGL(1,𝔽5)×C37⋊C3
commutator, hypocenterC5×C37C3×C4×C13
FrattiniC1G
Fitting, socleC5×C13×C37C3×C4
prime radicalD5×C13×C37⋊C3C2
cosocleD5×C37C2×C3×C13
LCSG ▷ C5×C37
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2405

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28860, 81);