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C₂×C₇₁₇₇ #28385154

order	14354
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7176
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₄₃₅₄
abelian	C₂×C₇₁₇₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14354 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₇₁₇₇, C₂×D₇₁₇₇
socle of	Dic₇₁₇₇, C₄×C₇₁₇₇, C₂×D₇₁₇₇
maximal subgroup of	Dic₇₁₇₇, C₄×C₇₁₇₇, C₂×D₇₁₇₇, …
maximal normal subgroup of	Dic₇₁₇₇, C₄×C₇₁₇₇, C₂×D₇₁₇₇, …
maximal quotient of	C₄×C₇₁₇₇, C₂²×C₇₁₇₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14354, 2);