Finite Group Databasebeta

← Prev (#37528591) Next (#37528593) →

C2×C5×D5×C11×ΓL(1,𝔽8) #37528592

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D5×C11×ΓL(1,𝔽8)
unambiguous semidirect productC5⋊(C22×C5×C11×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C5)⋊(C2×C5×C11×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×D5)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C5×C7×D5)⋊(C3×C11)
unambiguous semidirect product(C2×C5×C7×D5×C11)⋊C3

Splittings

Fitting, socleC2×C52×C7×C11 ⋊ C2×C3
derivedC5×C7 ⋊ C22×C3×C5×C11
HallC2×C5×C7×D5×C11 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C22
HallC52×C7×C11 ⋊ C22×C3
HallC2×C5×C7×D5 ⋊ C3×C11
HallC52×ΓL(1,𝔽8) ⋊ C22×C11
HallC52×C11 ⋊ C22×ΓL(1,𝔽8)
HallC52×C7 ⋊ C22×C3×C11
HallC7×C11 ⋊ C2×C3×C5×D5
SylowC52 ⋊ C22×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C3×C5×D5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C52×C7×C11C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C2×C5×C11

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

normal subgroups only

This group has 192 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 →

Presentation

transitive degreeμt(G) = 1540

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 403);