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C₉×C₁₉×D₉₇ #45684282

order	33174
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₉×D₉₇

Splittings

Fitting, Hall	C₉×C₁₉×C₉₇ ⋊ C₂
derived, Sylow	C₉₇ ⋊ C₂×C₉×C₁₉
Hall	C₁₉×C₉₇ ⋊ C₂×C₉
Hall	C₉×C₉₇ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	D₉₇
commutator, hypocenter	C₉₇	C₂×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×D₉₇
Fitting	C₉×C₁₉×C₉₇	C₂
socle	C₃×C₁₉×C₉₇	C₂×C₃
prime radical	C₃×C₁₉×D₉₇	C₃
cosocle	C₃×C₉₇	C₂×C₃×C₁₉
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₉×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16587

Conjugacy classes & character table

8550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33174, 6);