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C22×C7×C29⋊C7 #19150987

order5684
isoclinismisoclinic class of C29⋊C7
automorphism?
homologyAbelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC22×C7×C29⋊C7
unambiguous semidirect product(C22×C29)⋊C72
unambiguous semidirect product(C22×C7×C29)⋊C7

Splittings

Fitting, socleC22×C7×C29 ⋊ C7
derived, SylowC29 ⋊ C22×C72
HallC22×C29 ⋊ C72

Subgroups

subgroupG/H
center, hypercenterC22×C7C29⋊C7
commutator, hypocenterC29C22×C72
FrattiniC1G
Fitting, socleC22×C7×C29C7
LCSG ▷ C29
UCSC1 ◁ C22×C7

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×ΓL(1,𝔽8)×C29⋊C7, C7×A4×C29⋊C7, C22⋊ΓL(1,𝔽8)×C29⋊C7, …
maximal normal subgroup ofC22×ΓL(1,𝔽8)×C29⋊C7, C7×A4×C29⋊C7, C22⋊ΓL(1,𝔽8)×C29⋊C7, …
maximal quotient ofC2×D3×C7×C29⋊C7, C22×C3×C7×C29⋊C7, C2×C7×D5×C29⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5684, 34);