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C₂×C₅×D₇×#4294 #37560973

order	23940
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₅×D₇×#4294

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₇×C₁₉⋊C₃
commutator, hypocenter	C₇×C₁₉	C₂²×C₅×C₉
Frattini	C₃	C₂×C₅×D₇×C₁₉⋊C₃
Fitting, socle	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₅×D₇×C₁₉	C₃
cosocle	C₃×C₇×C₁₉	C₂²×C₃×C₅
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂×C₃×C₅

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11970

Conjugacy classes & character table

1350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 105);