Finite Group Databasebeta

← Prev (#37528586) Next (#37528588) →

C2×C52×C11×AGL(1,𝔽7) #37528587

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C52×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×C11×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C2×C3×C52×C11)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C52×C11)
unambiguous semidirect product(C2×D7)⋊(C3×C52×C11)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C52×C11)
unambiguous semidirect product(C2×C5×D7)⋊(C3×C5×C11)

Splittings

Fitting, socleC2×C52×C7×C11 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C52×C11
HallC2×C52×C11×D7 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C22
HallC52×C7×C11 ⋊ C22×C3
HallC2×C52×D7 ⋊ C3×C11
HallC52×ΓL(1,𝔽8) ⋊ C22×C11
HallC2×C11×D7 ⋊ C3×C52
HallC11×ΓL(1,𝔽8) ⋊ C22×C52
HallC52×C7 ⋊ C22×C3×C11
HallC7×C11 ⋊ C22×C3×C52
HallC2×D7 ⋊ C3×C52×C11
HallΓL(1,𝔽8) ⋊ C22×C52×C11

Subgroups

subgroupG/H
center, hypercenterC2×C52×C11AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C22×C3×C52×C11
FrattiniC1G
Fitting, socleC2×C52×C7×C11C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C52×C11

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3850

Conjugacy classes & character table

3850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 398);