Finite Group Databasebeta

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C7×C29⋊((C5⋊D5)⋊C3) #44478579

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

Aliases

direct productC7×C29⋊((C5⋊D5)⋊C3)

Splittings

Fitting, socle, HallC52×C7×C29 ⋊ C2×C3
derived, HallC52×C29 ⋊ C2×C3×C7
HallC7×C29×C52⋊C3 ⋊ C2
HallC7×C5⋊D145 ⋊ C3
HallC29×C52⋊C3 ⋊ C2×C7
HallC5⋊D145 ⋊ C3×C7
HallC7×C52⋊C3 ⋊ D29
HallC7×C29 ⋊ (C5⋊D5)⋊C3
HallC52×C7 ⋊ C3×D29
HallC52⋊C3 ⋊ C7×D29
SylowC29 ⋊ C7×(C5⋊D5)⋊C3
SylowC52 ⋊ C3×C7×D29

Subgroups

subgroupG/H
center, hypercenterC7C29⋊((C5⋊D5)⋊C3)
commutator, cosocle, hypocenterC52×C29C2×C3×C7
FrattiniC1G
Fitting, socleC52×C7×C29C2×C3
LCSG ▷ C52×C29
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3045

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 63);