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C4×C9×C41⋊C25 #49146604

order36900
automorphism?
homologyAbelianization (H1) = C4×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC4×C9×C41⋊C25
unambiguous semidirect product(C4×C41)⋊(C9×C25)
unambiguous semidirect product(C4×C9×C41)⋊C25

Splittings

derived, SylowC41 ⋊ C4×C9×C25
HallC4×C9×C41 ⋊ C25
HallC9×C41 ⋊ C4×C25
HallC4×C41 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC4×C5×C9C41⋊C5
commutator, hypocenterC41C4×C9×C25
FrattiniC2×C3×C5C2×C3×C41⋊C5
FittingC4×C5×C9×C41C5
socle, prime radical, cosocleC2×C3×C5×C41C2×C3×C5
LCSG ▷ C41
UCSC1 ◁ C4×C5×C9

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36900

Conjugacy classes & character table

2340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 5);