Finite Group Databasebeta

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C5×C11×D72 #24924758

order10780
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC5×C11×D72
unambiguous semidirect product(C7×D7)⋊(C2×C5×C11)
unambiguous semidirect product(C7⋊D7)⋊(C2×C5×C11)

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C22
derived, SylowC72 ⋊ C22×C5×C11
HallC72×C11 ⋊ C22×C5
HallC5×C72 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11D72
commutator, cosocle, hypocenterC72C22×C5×C11
FrattiniC1G
Fitting, socleC5×C72×C11C22
LCSG ▷ C72
UCSC1 ◁ C5×C11

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1375 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×#64418⋊C2, C5×C11×D7×AGL(1,𝔽7), C5×C11×#64423⋊C2, …
maximal normal subgroup ofC5×C11×D7×AGL(1,𝔽7), C5×C11×#64423⋊C2, C5×C11×#64422⋊C2, …
maximal quotient ofC3×C5×C11×D72, C5×C11×D7×D21, C5×C11×D21⋊D7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 71);