Finite Group Databasebeta

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C52⋊C3×D203 #44478573

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

Aliases

direct productC52⋊C3×D203
unambiguous semidirect productC29⋊(D7×C52⋊C3)

Splittings

Fitting, socle, derived, HallC52×C7×C29 ⋊ C2×C3
HallC7×C29×C52⋊C3 ⋊ C2
HallC52×D203 ⋊ C3
HallC29×C52⋊C3 ⋊ D7
HallC52×C29 ⋊ C3×D7
HallC7×C52⋊C3 ⋊ D29
HallC7×C29 ⋊ C2×C52⋊C3
HallC52×C7 ⋊ C3×D29
SylowC29 ⋊ D7×C52⋊C3
SylowC52 ⋊ C3×D203
SylowC7 ⋊ D29×C52⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7×C29C2×C3
LCSG ▷ C52×C7×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3045

Conjugacy classes & character table

1133 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 57);