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D5×C13×C121 #30628492

order15730
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C13×C121 · Schur multiplier (H2) = C1

Aliases

direct productD5×C13×C121
unambiguous semidirect productC5⋊(C2×C13×C121)

Splittings

Fitting, HallC5×C13×C121 ⋊ C2
derived, SylowC5 ⋊ C2×C13×C121
HallC5×C121 ⋊ C2×C13
HallC5×C13 ⋊ C2×C121

Subgroups

subgroupG/H
center, hypercenterC13×C121D5
commutator, hypocenterC5C2×C13×C121
FrattiniC11D5×C11×C13
FittingC5×C13×C121C2
socleC5×C11×C13C2×C11
prime radicalD5×C11×C13C11
cosocleC5×C11C2×C11×C13
LCSG ▷ C5
UCSC1 ◁ C13×C121

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7865

Conjugacy classes & character table

6292 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×AGL(1,𝔽5)×C121, C121×#63120, C13×C121⋊AGL(1,𝔽5), …
maximal normal subgroup ofC13×AGL(1,𝔽5)×C121, C121×#63120, C13×C121⋊AGL(1,𝔽5), …
maximal quotient ofC13×Dic5×C121, C2×D5×C13×C121

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15730, 9);