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C7×D11×C11⋊C5 #22555007

order8470
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D11×C11⋊C5

Splittings

Fitting, socle, HallC7×C112 ⋊ C2×C5
derived, SylowC112 ⋊ C2×C5×C7
HallC7×C11×C11⋊C5 ⋊ C2
HallC7×C11×D11 ⋊ C5
HallC11×C11⋊C5 ⋊ C2×C7
HallC11×D11 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC7D11×C11⋊C5
commutator, hypocenterC112C2×C5×C7
FrattiniC1G
Fitting, socleC7×C112C2×C5
LCSG ▷ C112
UCSC1 ◁ C7

34 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

343 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D11×AGL(1,𝔽11), D11×C7⋊AGL(1,𝔽11), D7×D11×C11⋊C5, …
maximal normal subgroup ofC7×D11×AGL(1,𝔽11), D11×C7⋊AGL(1,𝔽11), D7×D11×C11⋊C5, …
maximal quotient ofC7×Dic11×C11⋊C5, C2×C7×D11×C11⋊C5, C3×C7×D11×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8470, 23);