Finite Group Databasebeta

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C4×C5×C29⋊C49 #43249227

order28420
automorphism?
homologyAbelianization (H1) = C4×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C29⋊C49
unambiguous semidirect product(C4×C29)⋊(C5×C49)
unambiguous semidirect product(C4×C5×C29)⋊C49

Splittings

derived, SylowC29 ⋊ C4×C5×C49
HallC4×C5×C29 ⋊ C49
HallC5×C29 ⋊ C4×C49
HallC4×C29 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC4×C5×C7C29⋊C7
commutator, hypocenterC29C4×C5×C49
FrattiniC2×C7C2×C5×C29⋊C7
FittingC4×C5×C7×C29C7
socle, prime radicalC2×C5×C7×C29C2×C7
cosocleC2×C7×C29C2×C5×C7
LCSG ▷ C29
UCSC1 ◁ C4×C5×C7

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28420

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28420, 2);