Finite Group Databasebeta

← Prev (#22547603) Next (#22547605) →

C5×(C19⋊C3)⋊Dic7 #22547604

order7980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C19⋊C3)⋊Dic7
unambiguous semidirect product(C19⋊C3)⋊(C5×Dic7)

Splittings

derived, HallC7×C19 ⋊ C3×C4×C5
HallC5×Dic133 ⋊ C3
HallC5×C7×C19⋊C3 ⋊ C4
HallC5×C7×C19 ⋊ C3×C4
HallDic133 ⋊ C3×C5
HallC7×C19⋊C3 ⋊ C4×C5
HallC5×C19⋊C3 ⋊ Dic7
HallC5×C19 ⋊ C3×Dic7
HallC19⋊C3 ⋊ C5×Dic7
HallC5×C7 ⋊ (C19⋊C3)⋊C4
SylowC19 ⋊ C3×C5×Dic7
SylowC7 ⋊ C5×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5(C19⋊C3)⋊D7
commutator, hypocenterC7×C19C3×C4×C5
FrattiniC2C5×(C19⋊C3)⋊D7
Fitting, socleC2×C5×C7×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

360 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#18012151, C5×#18012152, C5×ΓL(1,𝔽8)⋊((C19⋊C3)⋊C4), …
maximal normal subgroup ofC5×#18012151, C5×#18012152, C5×ΓL(1,𝔽8)⋊((C19⋊C3)⋊C4), …
maximal quotient ofC5×#4294⋊Dic7, C3×C5×(C19⋊C3)⋊Dic7, C5×C3⋊((C19⋊C3)⋊Dic7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 29);