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C₂×C₁₉×#10620321 #38735692

order	24966
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₂×C₁₉×#10620321

Splittings

derived, Sylow	C₇₃ ⋊ C₂×C₉×C₁₉
Hall	C₂×C₁₉×C₇₃ ⋊ C₉
Hall	C₁₉×C₇₃ ⋊ C₂×C₉
Hall	C₂×C₇₃ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	C₇₃⋊C₃
commutator, hypocenter	C₇₃	C₂×C₉×C₁₉
Frattini	C₃	C₂×C₁₉×C₇₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₉×C₇₃	C₃
cosocle	C₃×C₇₃	C₂×C₃×C₁₉
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂×C₃×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 24966

Conjugacy classes & character table

3078 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24966, 2);