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C9×Dic53⋊C13 #37613579

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

Aliases

direct productC9×Dic53⋊C13
unambiguous semidirect productDic53⋊(C9×C13)
unambiguous semidirect product(C9×Dic53)⋊C13

Splittings

derived, SylowC53 ⋊ C4×C9×C13
HallC9×C53⋊C13 ⋊ C4
HallC9×Dic53 ⋊ C13
HallC53⋊C13 ⋊ C4×C9
HallC9×C53 ⋊ C4×C13
HallDic53 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC2×C9D53⋊C13
commutator, hypocenterC53C4×C9×C13
FrattiniC2×C3C3×D53⋊C13
FittingC2×C9×C53C2×C13
socle, cosocleC2×C3×C53C2×C3×C13
prime radicalC2×C3×C53⋊C13C2×C3
LCSG ▷ C53
UCSC1 ◁ C2×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1908

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 11);