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C9×C13×#6157 #37613604

order24804
automorphism?
homologyAbelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC9×C13×#6157

Splittings

Fitting, HallC9×C13×C53 ⋊ C4
derived, SylowC53 ⋊ C4×C9×C13
HallC13×C53 ⋊ C4×C9
HallC9×C53 ⋊ C4×C13

Subgroups

subgroupG/H
center, hypercenterC9×C13#6157
commutator, hypocenterC53C4×C9×C13
FrattiniC3C3×C13×#6157
FittingC9×C13×C53C4
socleC3×C13×C53C3×C4
prime radicalC3×C13×D53C2×C3
cosocleC3×D53C2×C3×C13
LCSG ▷ C53
UCSC1 ◁ C9×C13

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6201

Conjugacy classes & character table

1989 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 36);