Finite Group Databasebeta

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C7×C25×D87 #44478528

order30450
automorphism?
homologyAbelianization (H1) = C2×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×D87
unambiguous semidirect productC3⋊(C7×C25×D29)

Splittings

Fitting, HallC3×C7×C25×C29 ⋊ C2
derived, HallC3×C29 ⋊ C2×C7×C25
HallC7×C25×C29 ⋊ D3
HallC3×C25×C29 ⋊ C2×C7
HallC25×C29 ⋊ D3×C7
HallC3×C7×C29 ⋊ C2×C25
HallC3×C7×C25 ⋊ D29
HallC7×C29 ⋊ D3×C25
HallC3×C25 ⋊ C7×D29
SylowC29 ⋊ D3×C7×C25
HallC3×C7 ⋊ C25×D29
SylowC3 ⋊ C7×C25×D29

Subgroups

subgroupG/H
center, hypercenterC7×C25D87
commutator, hypocenterC3×C29C2×C7×C25
FrattiniC5C5×C7×D87
FittingC3×C7×C25×C29C2
socleC3×C5×C7×C29C2×C5
prime radicalC5×C7×D87C5
cosocleC3×C5×C29C2×C5×C7
LCSG ▷ C3×C29
UCSC1 ◁ C7×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15225

Conjugacy classes & character table

7875 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 12);