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D72×C11⋊C5 #24924747

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

Aliases

direct productD72×C11⋊C5
unambiguous semidirect product(C7×D7)⋊(C2×C11⋊C5)
unambiguous semidirect product(C7⋊D7)⋊(C2×C11⋊C5)
unambiguous semidirect product(C11×D72)⋊C5

Splittings

Fitting, socle, derived, HallC72×C11 ⋊ C22×C5
HallC72×C11⋊C5 ⋊ C22
HallC11×D72 ⋊ C5
SylowC72 ⋊ C22×C11⋊C5
SylowC11 ⋊ C5×D72

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C11C22×C5
LCSG ▷ C72×C11
UCSC1

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×#64418⋊C2, D7×AGL(1,𝔽7)×C11⋊C5, C11⋊C5×#64423⋊C2, …
maximal normal subgroup ofD7×AGL(1,𝔽7)×C11⋊C5, C11⋊C5×#64423⋊C2, C11⋊C5×#64422⋊C2, …
maximal quotient ofC3×D72×C11⋊C5, D7×D21×C11⋊C5, C11⋊C5×D21⋊D7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 60);