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C₂×C₅₃⋊(D₁₃⋊C₉) #37613602

order	24804
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅₃⋊(D₁₃⋊C₉)
unambiguous semidirect product	(C₂×C₅₃)⋊(D₁₃⋊C₉)
unambiguous semidirect product	(C₂×C₁₃⋊C₉)⋊D₅₃
unambiguous semidirect product	(C₂×D₆₈₉)⋊C₉

Splittings

derived, Hall	C₁₃×C₅₃ ⋊ C₂²×C₉
Hall	C₅₃×C₁₃⋊C₉ ⋊ C₂²
Hall	C₂×D₆₈₉ ⋊ C₉
Hall	C₁₃⋊C₉ ⋊ C₂×D₅₃
Sylow	C₅₃ ⋊ C₂×D₁₃⋊C₉
Sylow	C₁₃ ⋊ C₂×C₉×D₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₁₃⋊C₃)⋊D₅₃
commutator, hypocenter	C₁₃×C₅₃	C₂²×C₉
Frattini	C₃	C₂×(C₁₃⋊C₃)⋊D₅₃
Fitting, socle	C₂×C₃×C₁₃×C₅₃	C₂×C₃
prime radical	C₂×C₃×D₆₈₉	C₃
cosocle	C₃×C₁₃×C₅₃	C₂²×C₃
LCS	G ▷ C₁₃×C₅₃
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12402

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 34);