Finite Group Databasebeta

← Prev (#43274127) Next (#43274129) →

C13×Dic5×C37⋊C3 #43274128

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

Aliases

direct productC13×Dic5×C37⋊C3
unambiguous semidirect product(Dic5×C37)⋊(C3×C13)

Splittings

derived, HallC5×C37 ⋊ C3×C4×C13
HallC13×Dic5×C37 ⋊ C3
HallC5×C13×C37⋊C3 ⋊ C4
HallC5×C13×C37 ⋊ C3×C4
HallDic5×C37 ⋊ C3×C13
HallC5×C37⋊C3 ⋊ C4×C13
HallC13×C37 ⋊ C3×Dic5
HallC5×C13 ⋊ C4×C37⋊C3
SylowC37 ⋊ C3×C13×Dic5
SylowC5 ⋊ C4×C13×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C13D5×C37⋊C3
commutator, hypocenterC5×C37C3×C4×C13
FrattiniC2D5×C13×C37⋊C3
Fitting, socleC2×C5×C13×C37C2×C3
prime radicalC2×C5×C13×C37⋊C3C2
cosocleC2×C5×C37C2×C3×C13
LCSG ▷ C5×C37
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9620

Conjugacy classes & character table

1560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28860, 33);