Finite Group Databasebeta

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C2×C7×D5×C11⋊C5 #21440409

order7700
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D5×C11⋊C5
unambiguous semidirect productC5⋊(C22×C7×C11⋊C5)
unambiguous semidirect product(C2×C5)⋊(C2×C7×C11⋊C5)
unambiguous semidirect product(C2×D5×C11)⋊(C5×C7)
unambiguous semidirect product(C2×C7×D5×C11)⋊C5

Splittings

Fitting, socleC2×C5×C7×C11 ⋊ C2×C5
derivedC5×C11 ⋊ C22×C5×C7
HallC5×C7×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C22×C7
HallC7×C11 ⋊ C2×C5×D5
SylowC11 ⋊ C2×C5×C7×D5

Subgroups

subgroupG/H
center, hypercenterC2×C7D5×C11⋊C5
commutator, hypocenterC5×C11C22×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C11C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C2×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

392 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D5×ΓL(1,𝔽8)×C11⋊C5, D3×C7×D5×C11⋊C5, C2×C3×C7×D5×C11⋊C5, …
maximal normal subgroup ofC2×D5×ΓL(1,𝔽8)×C11⋊C5, C2×C3×C7×D5×C11⋊C5
maximal quotient ofD3×C7×D5×C11⋊C5, C2×C3×C7×D5×C11⋊C5, C2×C7×D15×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 73);