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C₅²×C₁₉×Dic₁₃ #37590802

order	24700
automorphism	?
homology	Abelianization (H₁) = C₄×C₅²×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

C₅²×C₁₉×Dic₁₃

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₅²×C₁₉
Hall	C₅²×C₁₃×C₁₉ ⋊ C₄
Hall	C₅²×C₁₃ ⋊ C₄×C₁₉
Hall	C₁₃×C₁₉ ⋊ C₄×C₅²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₁₉	D₁₃
commutator, hypocenter	C₁₃	C₄×C₅²×C₁₉
Frattini	C₂	C₅²×C₁₉×D₁₃
Fitting, socle, prime radical	C₂×C₅²×C₁₃×C₁₉	C₂
cosocle	C₂×C₁₃	C₂×C₅²×C₁₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₅²×C₁₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 24700

Conjugacy classes & character table

7600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24700, 46);