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C₂×C₇⋊C₉×C₁₉₇ #37613896

order	24822
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₇⋊C₉×C₁₉₇
unambiguous semidirect product	(C₂×C₇)⋊(C₉×C₁₉₇)
unambiguous semidirect product	(C₂×C₇×C₁₉₇)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₁₉₇
Hall	C₂×C₇×C₁₉₇ ⋊ C₉
Hall	C₇×C₁₉₇ ⋊ C₂×C₉
Hall	C₂×C₇ ⋊ C₉×C₁₉₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉₇	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂×C₉×C₁₉₇
Frattini	C₃	C₂×ΓL(1,𝔽₈)×C₁₉₇
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₉₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₉₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₁₉₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 24822

Conjugacy classes & character table

5910 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24822, 3);