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C₃×D₇×C₁₉₇ #22552010

order	8274
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉₇ · Schur multiplier (H₂) = C₁

Aliases

C₃×D₇×C₁₉₇

Splittings

Fitting, socle, Hall	C₃×C₇×C₁₉₇ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₃×C₁₉₇
Hall	C₇×C₁₉₇ ⋊ C₂×C₃
Hall	C₃×C₇ ⋊ C₂×C₁₉₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉₇	D₇
commutator, hypocenter	C₇	C₂×C₃×C₁₉₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₉₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₉₇

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2955 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₇×D₁₉₇, D₃×D₇×C₁₉₇, D₇×D₅₉₁, …
maximal normal subgroup of	C₃×D₇×D₁₉₇, D₃×D₇×C₁₉₇, D₇×D₅₉₁, …
maximal quotient of	C₃×Dic₇×C₁₉₇, C₂×C₃×D₇×C₁₉₇, C₉×D₇×C₁₉₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8274, 5);