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D5×D7×C11⋊C5 #21440404

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

Aliases

direct productD5×D7×C11⋊C5
unambiguous semidirect product(C7×D5)⋊(C2×C11⋊C5)
unambiguous semidirect product(C5×D7)⋊(C2×C11⋊C5)
unambiguous semidirect productD35⋊(C2×C11⋊C5)
unambiguous semidirect product(D5×C11×D7)⋊C5

Splittings

Fitting, socle, derivedC5×C7×C11 ⋊ C22×C5
HallC5×C7×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C2×D7
HallC7×C11 ⋊ C2×C5×D5
SylowC11 ⋊ C5×D5×D7
SylowC7 ⋊ C2×D5×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C11C22×C5
LCSG ▷ C5×C7×C11
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×AGL(1,𝔽7)×C11⋊C5, C3×D5×D7×C11⋊C5, D7×D15×C11⋊C5, …
maximal normal subgroup ofD5×AGL(1,𝔽7)×C11⋊C5, C3×D5×D7×C11⋊C5
maximal quotient ofC3×D5×D7×C11⋊C5, D7×D15×C11⋊C5, D5×D21×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 68);