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C5×C7×D7×D11 #24924756

order10780
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×D7×D11

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C22
derivedC7×C11 ⋊ C22×C5×C7
HallC72×C11 ⋊ C22×C5
HallC5×C72 ⋊ C2×D11
HallC5×C11 ⋊ C2×C7×D7
SylowC72 ⋊ C2×C5×D11
SylowC11 ⋊ C2×C5×C7×D7

Subgroups

subgroupG/H
center, hypercenterC5×C7D7×D11
commutator, cosocle, hypocenterC7×C11C22×C5×C7
FrattiniC1G
Fitting, socleC5×C72×C11C22
LCSG ▷ C7×C11
UCSC1 ◁ C5×C7

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1225 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D11×#64418, C5×C7×D11×AGL(1,𝔽7), C5×D7×ΓL(1,𝔽8)×D11, …
maximal normal subgroup ofC5×C7×D11×AGL(1,𝔽7), C5×D7×ΓL(1,𝔽8)×D11, C5×D11×#64423, …
maximal quotient ofC3×C5×C7×D7×D11, C5×C7×D11×D21, C5×C7×D7×D33, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 69);