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#442×C₉₇ #20260309

order	6208
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₉₇ · Schur multiplier (H₂) = C₂³

Aliases

Subgroups

	subgroup	G/H
center, socle	C₂²×C₉₇	C₂×D₄
commutator	C₄	C₂²×C₄×C₉₇
Frattini, cosocle	C₂×C₄	C₂³×C₉₇
prime radical	C₂×D₈×C₉₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉₇ ◁ C₄²×C₉₇ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2134 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉₇×AGL(1,ℤ/16), C₂×#442×C₉₇, C₉₇×#2943, …
maximal normal subgroup of	C₉₇×AGL(1,ℤ/16), C₂×#442×C₉₇, C₉₇×#2943, …
maximal quotient of	C₉₇×#1580, C₉₇×#1586, C₉₇×#1594, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 123);