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C13×Dic9×C53 #37613575

order24804
automorphism?
homologyAbelianization (H1) = C4×C13×C53 · Schur multiplier (H2) = C1

Aliases

direct productC13×Dic9×C53
unambiguous semidirect productC9⋊(C4×C13×C53)

Splittings

derived, SylowC9 ⋊ C4×C13×C53
HallC9×C13×C53 ⋊ C4
HallC9×C53 ⋊ C4×C13
HallC9×C13 ⋊ C4×C53

Subgroups

subgroupG/H
center, hypercenterC2×C13×C53D9
commutator, hypocenterC9C4×C13×C53
FrattiniC2×C3D3×C13×C53
FittingC2×C9×C13×C53C2
socle, prime radicalC2×C3×C13×C53D3
cosocleC2×C9C2×C13×C53
LCSG ▷ C9
UCSC1 ◁ C2×C13×C53

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24804

Conjugacy classes & character table

8268 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 7);