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C5×C29×Dic49 #43249229

order28420
automorphism?
homologyAbelianization (H1) = C4×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29×Dic49
unambiguous semidirect productC49⋊(C4×C5×C29)

Splittings

derived, SylowC49 ⋊ C4×C5×C29
HallC5×C29×C49 ⋊ C4
HallC29×C49 ⋊ C4×C5
HallC5×C49 ⋊ C4×C29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C29D49
commutator, hypocenterC49C4×C5×C29
FrattiniC2×C7C5×D7×C29
FittingC2×C5×C29×C49C2
socle, prime radicalC2×C5×C7×C29D7
cosocleC2×C49C2×C5×C29
LCSG ▷ C49
UCSC1 ◁ C2×C5×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28420

Conjugacy classes & character table

7540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28420, 4);