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C32×D5×C29⋊C7 #32912498

order18270
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×D5×C29⋊C7
unambiguous semidirect productC5⋊(C2×C32×C29⋊C7)
unambiguous semidirect product(D5×C29)⋊(C32×C7)
unambiguous semidirect product(C3×D5×C29)⋊(C3×C7)
unambiguous semidirect product(C32×D5×C29)⋊C7

Splittings

Fitting, socle, HallC32×C5×C29 ⋊ C2×C7
derived, HallC5×C29 ⋊ C2×C32×C7
HallC32×C5×C29⋊C7 ⋊ C2
HallC32×D5×C29 ⋊ C7
HallC5×C29⋊C7 ⋊ C2×C32
HallD5×C29 ⋊ C32×C7
HallC32×C29 ⋊ C7×D5
HallC32×C5 ⋊ C2×C29⋊C7
SylowC29 ⋊ C32×C7×D5
SylowC5 ⋊ C2×C32×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC32D5×C29⋊C7
commutator, cosocle, hypocenterC5×C29C2×C32×C7
FrattiniC1G
Fitting, socleC32×C5×C29C2×C7
LCSG ▷ C5×C29
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1305

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC32×#10596816⋊C7, C32×AGL(1,𝔽5)×C29⋊C7, C32×D5×D29⋊C7, …
maximal normal subgroup ofC32×#10596816⋊C7, C32×AGL(1,𝔽5)×C29⋊C7, C32×D5×D29⋊C7, …
maximal quotient ofC32×Dic5×C29⋊C7, C2×C32×D5×C29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 36);