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(C29⋊C7)⋊((C5⋊D5)⋊C3) #44478553

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C5

Aliases

unambiguous semidirect product(C29⋊C7)⋊((C5⋊D5)⋊C3)
unambiguous semidirect product(C29⋊((C5⋊D5)⋊C3))⋊C7
unambiguous semidirect product(C5⋊(C5⋊(D29⋊C7)))⋊C3

Splittings

Fitting, socle, derived, HallC52×C29 ⋊ C2×C3×C7
HallC52⋊C3×C29⋊C7 ⋊ C2
HallC5⋊(C5⋊(D29⋊C7)) ⋊ C3
HallC52×C29⋊C7 ⋊ C2×C3
HallC29⋊((C5⋊D5)⋊C3) ⋊ C7
HallC29×C52⋊C3 ⋊ C2×C7
HallC5⋊D145 ⋊ C3×C7
HallC29⋊C7 ⋊ (C5⋊D5)⋊C3
HallC52⋊C3 ⋊ D29⋊C7
SylowC29 ⋊ C7×(C5⋊D5)⋊C3
SylowC52 ⋊ C3×D29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C29C2×C3×C7
LCSG ▷ C52×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 435

Polycyclic presentation:

2,3,7,5^2,29|d^a=d^4,e^a=e^4,f^a=f^28,d^b=de,e^b=d^2e^3,f^c=f^16

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 37);