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C11×AGL(1,𝔽7)×C5⋊D5 #37528541

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

Aliases

direct productC11×AGL(1,𝔽7)×C5⋊D5
unambiguous semidirect productD7⋊(C3×C11×C5⋊D5)
unambiguous semidirect product(C5×AGL(1,𝔽7))⋊(D5×C11)

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C22×C3
derived, HallC52×C7 ⋊ C22×C3×C11
HallC11×D7×C5⋊D5 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C22
HallD7×C5⋊D5 ⋊ C3×C11
HallC52×ΓL(1,𝔽8) ⋊ C22×C11
HallC52×C11 ⋊ C2×AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ C2×C5⋊D5
HallC7×C11 ⋊ C2×C3×C5⋊D5
SylowC52 ⋊ C2×C11×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×C11×C5⋊D5
SylowC7 ⋊ C2×C3×C11×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC11AGL(1,𝔽7)×C5⋊D5
commutator, cosocle, hypocenterC52×C7C22×C3×C11
FrattiniC1G
Fitting, socleC52×C7×C11C22×C3
LCSG ▷ C52×C7
UCSC1 ◁ C11

320 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 1925

Conjugacy classes & character table

1078 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 352);