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C2×C5×D7×C11⋊C5 #21440407

order7700
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5×D7×C11⋊C5
unambiguous semidirect productC7⋊(C22×C5×C11⋊C5)
unambiguous semidirect product(C2×C7)⋊(C2×C5×C11⋊C5)
unambiguous semidirect product(C2×C11×D7)⋊C52
unambiguous semidirect product(C2×C5×C11×D7)⋊C5

Splittings

Fitting, socleC2×C5×C7×C11 ⋊ C2×C5
derived, HallC7×C11 ⋊ C22×C52
HallC5×C7×C11⋊C5 ⋊ C22
HallC2×C11×D7 ⋊ C52
SylowC11 ⋊ C2×C52×D7
SylowC7 ⋊ C22×C5×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C5D7×C11⋊C5
commutator, hypocenterC7×C11C22×C52
FrattiniC1G
Fitting, socleC2×C5×C7×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

350 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×AGL(1,𝔽7)×C11⋊C5, C5×D3×D7×C11⋊C5, C2×C3×C5×D7×C11⋊C5, …
maximal normal subgroup ofC2×C5×AGL(1,𝔽7)×C11⋊C5, C2×C3×C5×D7×C11⋊C5
maximal quotient ofC5×D3×D7×C11⋊C5, C2×C3×C5×D7×C11⋊C5, C2×C5×D21×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 71);