Finite Group Databasebeta

← Prev (#28413408) Next (#28413410) →

C2×C5×C7×D5×ΓL(1,𝔽8) #28413409

order14700
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D5×ΓL(1,𝔽8)
unambiguous semidirect productC5⋊(C22×C5×C7×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C5)⋊(C2×C5×C7×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×D5)⋊(C3×C5×C7)
unambiguous semidirect product(C2×C5×C7×D5)⋊(C3×C7)

Splittings

Fitting, socleC2×C52×C72 ⋊ C2×C3
derivedC5×C7 ⋊ C22×C3×C5×C7
HallC2×C5×C72×D5 ⋊ C3
HallC52×C7×ΓL(1,𝔽8) ⋊ C22
HallC52×C72 ⋊ C22×C3
SylowC72 ⋊ C2×C3×C5×D5
SylowC52 ⋊ C22×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C52×C72C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C2×C5×C7

240 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 588);