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C2×C11⋊C5×C5⋊AGL(1,𝔽7) #37528424

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

Aliases

direct productC2×C11⋊C5×C5⋊AGL(1,𝔽7)
unambiguous semidirect product(C2×C5)⋊(AGL(1,𝔽7)×C11⋊C5)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(D5×C11⋊C5)
unambiguous semidirect product(C2×D35)⋊(C3×C11⋊C5)
unambiguous semidirect product(C2×C11×C5⋊AGL(1,𝔽7))⋊C5
unambiguous semidirect product(C2×C11⋊C5×D35)⋊C3

Splittings

Fitting, socleC2×C5×C7×C11 ⋊ C2×C3×C5
derivedC5×C7×C11 ⋊ C22×C3×C5
HallC2×C11⋊C5×D35 ⋊ C3
HallC5×ΓL(1,𝔽8)×C11⋊C5 ⋊ C22
HallC5×C7×C11⋊C5 ⋊ C22×C3
HallC5×C11⋊C5 ⋊ C2×AGL(1,𝔽7)
HallC11×ΓL(1,𝔽8) ⋊ C2×C5×D5
HallC7×C11 ⋊ C2×C3×C5×D5
HallΓL(1,𝔽8) ⋊ C2×D5×C11⋊C5
SylowC11 ⋊ C2×C5×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×D5×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7×C11C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C11C2×C3×C5
LCSG ▷ C5×C7×C11
UCSC1 ◁ C2

192 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 770

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 235);