Finite Group Databasebeta

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C25×Dic9×C41 #49146608

order36900
automorphism?
homologyAbelianization (H1) = C4×C25×C41 · Schur multiplier (H2) = C1

Aliases

direct productC25×Dic9×C41
unambiguous semidirect productC9⋊(C4×C25×C41)

Splittings

derived, SylowC9 ⋊ C4×C25×C41
HallC9×C25×C41 ⋊ C4
HallC9×C41 ⋊ C4×C25
HallC9×C25 ⋊ C4×C41

Subgroups

subgroupG/H
center, hypercenterC2×C25×C41D9
commutator, hypocenterC9C4×C25×C41
FrattiniC2×C3×C5C5×D3×C41
FittingC2×C9×C25×C41C2
socle, prime radicalC2×C3×C5×C41C5×D3
cosocleC2×C5×C9C2×C5×C41
LCSG ▷ C9
UCSC1 ◁ C2×C25×C41

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36900

Conjugacy classes & character table

12300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 9);