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C4×C13×C29⋊C7 #24902198

order10556
isoclinismisoclinic class of C29⋊C7
automorphism?
homologyAbelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×C29⋊C7
unambiguous semidirect product(C4×C29)⋊(C7×C13)
unambiguous semidirect product(C4×C13×C29)⋊C7

Splittings

Fitting, HallC4×C13×C29 ⋊ C7
derived, SylowC29 ⋊ C4×C7×C13
HallC13×C29 ⋊ C4×C7
HallC4×C29 ⋊ C7×C13

Subgroups

subgroupG/H
center, hypercenterC4×C13C29⋊C7
commutator, hypocenterC29C4×C7×C13
FrattiniC2C2×C13×C29⋊C7
FittingC4×C13×C29C7
socleC2×C13×C29C2×C7
prime radicalC2×C13×C29⋊C7C2
cosocleC2×C29C2×C7×C13
LCSG ▷ C29
UCSC1 ◁ C4×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×C13×C29⋊C7, C4×C13⋊C3×C29⋊C7, Dic3×C13×C29⋊C7
maximal normal subgroup ofC3×C4×C13×C29⋊C7, C4×C13⋊C3×C29⋊C7
maximal quotient ofC3×C4×C13×C29⋊C7, Dic3×C13×C29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10556, 2);