Finite Group Databasebeta

← Prev (#29509336) Next (#29509338) →

C₂×C₇₇₅₇ #29509337

order	15514
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7756
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₅₅₁₄
abelian	C₂×C₇₇₅₇

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

15514 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₇₇₅₇, C₂×D₇₇₅₇
socle of	Dic₇₇₅₇, C₄×C₇₇₅₇, C₂×D₇₇₅₇
maximal subgroup of	Dic₇₇₅₇, C₄×C₇₇₅₇, C₂×D₇₇₅₇, …
maximal normal subgroup of	Dic₇₇₅₇, C₄×C₇₇₅₇, C₂×D₇₇₅₇, …
maximal quotient of	C₄×C₇₇₅₇, C₂²×C₇₇₅₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15514, 2);