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C29×#11760384 #44478584

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C5

Aliases

direct productC29×#11760384

Splittings

Fitting, socle, HallC52×C7×C29 ⋊ C2×C3
derived, HallC52×C7 ⋊ C2×C3×C29
HallC7×C29×C52⋊C3 ⋊ C2
HallC29×C5⋊D35 ⋊ C3
HallC29×C52⋊C3 ⋊ D7
HallC52×C29 ⋊ C3×D7
HallC7×C52⋊C3 ⋊ C2×C29
HallC5⋊D35 ⋊ C3×C29
HallC7×C29 ⋊ (C5⋊D5)⋊C3
HallC52⋊C3 ⋊ D7×C29
SylowC52 ⋊ C3×D7×C29
SylowC7 ⋊ C29×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC29#11760384
commutator, cosocle, hypocenterC52×C7C2×C3×C29
FrattiniC1G
Fitting, socleC52×C7×C29C2×C3
LCSG ▷ C52×C7
UCSC1 ◁ C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3045

Conjugacy classes & character table

1247 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 68);