Finite Group Databasebeta

← Prev (#19129682) Next (#19129684) →

C5×Dic7×C13⋊C3 #19129683

order5460
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic7×C13⋊C3

Splittings

derived, HallC7×C13 ⋊ C3×C4×C5
HallC5×C13×Dic7 ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C4
HallC5×C7×C13 ⋊ C3×C4
HallC13×Dic7 ⋊ C3×C5
HallC7×C13⋊C3 ⋊ C4×C5
HallC5×C13 ⋊ C3×Dic7
HallC5×C7 ⋊ C4×C13⋊C3
SylowC13 ⋊ C3×C5×Dic7
SylowC7 ⋊ C4×C5×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5D7×C13⋊C3
commutator, hypocenterC7×C13C3×C4×C5
FrattiniC2C5×D7×C13⋊C3
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

350 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C13⋊C3×ΓL(1,𝔽8)⋊C4, C3×C5×Dic7×C13⋊C3, C5×C13⋊C3×Dic21, …
maximal normal subgroup ofC5×C13⋊C3×ΓL(1,𝔽8)⋊C4, C3×C5×Dic7×C13⋊C3, C25×Dic7×C13⋊C3, …
maximal quotient ofC5×Dic7×C13⋊C9, C3×C5×Dic7×C13⋊C3, C5×C13⋊C3×Dic21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 25);