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C7×AGL(1,𝔽5)×C11⋊C5 #21440396

order7700
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×AGL(1,𝔽5)×C11⋊C5
unambiguous semidirect product(C11×AGL(1,𝔽5))⋊(C5×C7)
unambiguous semidirect product(C7×C11×AGL(1,𝔽5))⋊C5

Splittings

Fitting, socleC5×C7×C11 ⋊ C4×C5
derivedC5×C11 ⋊ C4×C5×C7
HallC5×C7×C11⋊C5 ⋊ C4
HallC5×C11⋊C5 ⋊ C4×C7
HallC7×C11 ⋊ C5×AGL(1,𝔽5)
SylowC11 ⋊ C5×C7×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC7AGL(1,𝔽5)×C11⋊C5
commutator, hypocenterC5×C11C4×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C11C4×C5
LCSG ▷ C5×C11
UCSC1 ◁ C7

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×ΓL(1,𝔽8)×C11⋊C5, C3×C7×AGL(1,𝔽5)×C11⋊C5, C7×C11⋊C5×ΓL(1,𝔽16)
maximal normal subgroup ofAGL(1,𝔽5)×ΓL(1,𝔽8)×C11⋊C5, C3×C7×AGL(1,𝔽5)×C11⋊C5
maximal quotient ofC3×C7×AGL(1,𝔽5)×C11⋊C5, C7×C11⋊C5×ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 60);