Finite Group Databasebeta

← Prev (#22554988) Next (#22554990) →

C2×C7×C121⋊C5 #22554989

order8470
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7×C121⋊C5
unambiguous semidirect product(C2×C121)⋊(C5×C7)
unambiguous semidirect product(C2×C7×C121)⋊C5

Splittings

Fitting, HallC2×C7×C121 ⋊ C5
derived, SylowC121 ⋊ C2×C5×C7
HallC7×C121 ⋊ C2×C5
HallC2×C121 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7C121⋊C5
commutator, hypocenterC121C2×C5×C7
FrattiniC11C2×C7×C11⋊C5
FittingC2×C7×C121C5
socleC2×C7×C11C11⋊C5
LCSG ▷ C121
UCSC1 ◁ C2×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

406 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×Dic121⋊C5, Dic7×C121⋊C5, C7⋊(Dic121⋊C5), …
maximal normal subgroup ofC7×Dic121⋊C5, Dic7×C121⋊C5, C7⋊(Dic121⋊C5), …
maximal quotient ofC4×C7×C121⋊C5, C22×C7×C121⋊C5, C2×C3×C7×C121⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8470, 5);