Finite Group Databasebeta

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C2×C3×C5×C29⋊C7 #20259016

order6090
isoclinismisoclinic class of C29⋊C7
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C5×C29⋊C7
unambiguous semidirect product(C2×C29)⋊(C3×C5×C7)
unambiguous semidirect product(C2×C3×C29)⋊(C5×C7)
unambiguous semidirect product(C2×C5×C29)⋊(C3×C7)
unambiguous semidirect product(C2×C3×C5×C29)⋊C7

Splittings

Fitting, socle, HallC2×C3×C5×C29 ⋊ C7
derived, SylowC29 ⋊ C2×C3×C5×C7
HallC3×C5×C29 ⋊ C2×C7
HallC2×C5×C29 ⋊ C3×C7
HallC2×C3×C29 ⋊ C5×C7
HallC5×C29 ⋊ C2×C3×C7
HallC3×C29 ⋊ C2×C5×C7
HallC2×C29 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C29⋊C7
commutator, hypocenterC29C2×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C29C7
LCSG ▷ C29
UCSC1 ◁ C2×C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

330 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×C9×C29⋊C7, C3×C5×D3×C29⋊C7, C2×C32×C5×C29⋊C7, …
maximal normal subgroup ofC2×C5×C9×C29⋊C7, C2×C32×C5×C29⋊C7, C2×C3×C25×C29⋊C7, …
maximal quotient ofC2×C5×C9×C29⋊C7, C3×C5×D3×C29⋊C7, C2×C32×C5×C29⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6090, 2);