Finite Group Databasebeta

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C5×C13⋊C3×#3866 #43274170

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

Aliases

direct productC5×C13⋊C3×#3866

Splittings

Fitting, socle, HallC5×C13×C37 ⋊ C3×C4
derived, HallC13×C37 ⋊ C3×C4×C5
HallC5×C13×#3866 ⋊ C3
HallC5×C37×C13⋊C3 ⋊ C4
HallC13×#3866 ⋊ C3×C5
HallC37×C13⋊C3 ⋊ C4×C5
HallC5×C37 ⋊ C4×C13⋊C3
HallC5×C13 ⋊ C3×#3866
SylowC37 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C3×C5×#3866

Subgroups

subgroupG/H
center, hypercenterC5C13⋊C3×#3866
commutator, hypocenterC13×C37C3×C4×C5
FrattiniC1G
Fitting, socleC5×C13×C37C3×C4
prime radicalC5×C13⋊C3×D37C2
cosocleC13×D37C2×C3×C5
LCSG ▷ C13×C37
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2405

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28860, 75);