Finite Group Databasebeta

← Prev (#19129670) Next (#19129672) →

C5×C7×Dic3×C13 #19129671

order5460
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic3×C13
unambiguous semidirect productC3⋊(C4×C5×C7×C13)

Splittings

derived, SylowC3 ⋊ C4×C5×C7×C13
HallC3×C5×C7×C13 ⋊ C4
HallC3×C7×C13 ⋊ C4×C5
HallC3×C5×C13 ⋊ C4×C7
HallC3×C5×C7 ⋊ C4×C13
HallC3×C13 ⋊ C4×C5×C7
HallC3×C7 ⋊ C4×C5×C13
HallC3×C5 ⋊ C4×C7×C13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C13D3
commutator, hypocenterC3C4×C5×C7×C13
FrattiniC2C5×D3×C7×C13
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C3
UCSC1 ◁ C2×C5×C7×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2730 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×C13×Dic9, C5×C7×Dic3×C13⋊C3, C5×Dic3×C13×ΓL(1,𝔽8), …
maximal normal subgroup ofC5×C7×Dic3×C13⋊C3, C5×Dic3×C13×ΓL(1,𝔽8), C5×Dic3×#63270, …
maximal quotient ofC5×C7×C13×Dic9, C3×C5×C7×Dic3×C13, C5×C7×C13×C3⋊Dic3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 13);