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#261×C₁₉₇ #23779581

order	10244
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉₇ · Schur multiplier (H₂) = C₁

Aliases

#261×C₁₉₇

Splittings

Fitting, socle, Hall	C₁₃×C₁₉₇ ⋊ C₄
derived, Sylow	C₁₃ ⋊ C₄×C₁₉₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉₇	#261
commutator, hypocenter	C₁₃	C₄×C₁₉₇
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₉₇	C₄
prime radical	D₁₃×C₁₉₇	C₂
cosocle	D₁₃	C₂×C₁₉₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₉₇

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1379 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	AGL(1,𝔽₁₃)×C₁₉₇, C₃×#261×C₁₉₇, C₃⋊#261×C₁₉₇
maximal normal subgroup of	AGL(1,𝔽₁₃)×C₁₉₇, C₃×#261×C₁₉₇
maximal quotient of	C₃×#261×C₁₉₇, C₃⋊#261×C₁₉₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10244, 7);