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C5×#19153499 #43274153

order28860
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#19153499

Splittings

Fitting, socle, HallC5×C13×C37 ⋊ C3×C4
derived, HallC13×C37 ⋊ C3×C4×C5
HallC5×#14515321 ⋊ C3
HallC5×C37×C13⋊C3 ⋊ C4
Hall#14515321 ⋊ C3×C5
HallC37×C13⋊C3 ⋊ C4×C5
HallC5×C13⋊C3 ⋊ #3866
HallC5×C37 ⋊ AGL(1,𝔽13)
HallC5×C13 ⋊ C3×#3866
HallC13⋊C3 ⋊ C5×#3866
SylowC37 ⋊ C5×AGL(1,𝔽13)
SylowC13 ⋊ C3×C5×#3866

Subgroups

subgroupG/H
center, hypercenterC5#19153499
commutator, hypocenterC13×C37C3×C4×C5
FrattiniC1G
Fitting, socleC5×C13×C37C3×C4
prime radicalC5×(C13⋊C3)⋊D37C2
cosocleD481C2×C3×C5
LCSG ▷ C13×C37
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2405

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28860, 58);