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#347×C₁₄₉ #23749104

order	9536
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₄₉ · Schur multiplier (H₂) = C₁

Aliases

#347×C₁₄₉

Subgroups

	subgroup	G/H
center	C₄×C₁₄₉	C₄²
commutator	C₄	C₄²×C₁₄₉
Frattini, cosocle	C₂×C₈	C₂²×C₁₄₉
socle	C₂×C₁₄₉	#97
prime radical	C₂²×C₁₄₉	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₄₉ ◁ G

46 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3278 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#34042723, #34042725, #347×D₁₄₉, …
maximal subgroup of	#1355×C₁₄₉, #1356×C₁₄₉, C₂×#347×C₁₄₉, …
maximal normal subgroup of	#1355×C₁₄₉, #1356×C₁₄₉, C₂×#347×C₁₄₉, …
maximal quotient of	#1313×C₁₄₉, #1375×C₁₄₉, C₂×#347×C₁₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 28);