Finite Group Databasebeta

← Prev (#26046213) Next (#26046215) →

C2×C3×C5×#87705 #26046214

order11970
isoclinismisoclinic class of #87705
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×#87705

Splittings

Fitting, socleC2×C3×C5×C7×C19 ⋊ C3
derived, HallC7×C19 ⋊ C2×C32×C5
HallC2×C5×C7×C19 ⋊ C32
HallC5×C7×C19 ⋊ C2×C32
HallC2×C7×C19 ⋊ C32×C5
HallC2×C5×C19 ⋊ C3×ΓL(1,𝔽8)
HallC5×C19 ⋊ C2×C3×ΓL(1,𝔽8)
HallC2×C5×C7 ⋊ C3×C19⋊C3
HallC2×C19 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×C19⋊C3
SylowC19 ⋊ C2×C3×C5×ΓL(1,𝔽8)
HallC2×C7 ⋊ C3×C5×C19⋊C3
SylowC7 ⋊ C2×C3×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5#87705
commutator, cosocle, hypocenterC7×C19C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C19C3
LCSG ▷ C7×C19
UCSC1 ◁ C2×C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1410 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×#13097589, C3×C5×#13097587, C3×C5×#13097583, …
maximal normal subgroup ofC3×C5×#13097589, C3×C5×#13097587, C3×C5×#13097583, …
maximal quotient ofC3×C4×C5×#87705, C22×C3×C5×#87705

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 143);