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C₂×#17984641 #22580251

order	8892
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×#17984641

Splittings

Fitting, socle	C₂×C₁₃×C₁₉ ⋊ C₂×C₉
derived, Hall	C₁₃×C₁₉ ⋊ C₂²×C₉
Hall	#14555740 ⋊ C₂²
Hall	C₂×C₁₉×D₁₃ ⋊ C₉
Hall	C₂×D₁₃ ⋊ #4296
Sylow	C₁₉ ⋊ C₂×D₁₃⋊C₉
Sylow	C₁₃ ⋊ C₂²×#4296

Subgroups

	subgroup	G/H
center, hypercenter	C₂	#17984641
commutator, hypocenter	C₁₃×C₁₉	C₂²×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₁₉	C₂×C₉
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 154);