Finite Group Databasebeta

← Prev (#22547606) Next (#22547608) →

C5×#13097589 #22547607

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

Aliases

direct productC5×#13097589

Splittings

derived, HallC7×C19 ⋊ C3×C4×C5
HallC5×Dic133 ⋊ C3
HallC5×#87705 ⋊ C4
HallC5×C7×C19 ⋊ C3×C4
HallDic133 ⋊ C3×C5
Hall#87705 ⋊ C4×C5
HallC5×C19 ⋊ ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ (C19⋊C3)⋊C4
SylowC19 ⋊ C5×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C5×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5#11716328
commutator, hypocenterC7×C19C3×C4×C5
FrattiniC2C5×#11716328
Fitting, socleC2×C5×C7×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

280 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×ΓL(1,𝔽8)⋊((C19⋊C3)⋊C4), C3×C5×#13097589, C5×C3⋊#13097589
maximal normal subgroup ofC5×ΓL(1,𝔽8)⋊((C19⋊C3)⋊C4), C3×C5×#13097589
maximal quotient ofC5×#18012097, C3×C5×#13097589, C5×C3⋊#13097589

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 32);