Finite Group Databasebeta

← Prev (#72184870) Next (#72184872) →

C₂×C₈×C₁₃×C₂₇ #72184871

order	5616
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂×C₈×C₁₃×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₉	C₂²×C₃×C₁₃
socle, prime radical	C₂²×C₃×C₁₃	C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₃×C₁₆×C₂₇, C₄×C₈×C₁₃×C₂₇, C₂²×C₈×C₁₃×C₂₇, …
maximal normal subgroup of	C₂×C₁₃×C₁₆×C₂₇, C₄×C₈×C₁₃×C₂₇, C₂²×C₈×C₁₃×C₂₇, …
maximal quotient of	C₂×C₁₃×C₁₆×C₂₇, C₄×C₈×C₁₃×C₂₇, C₂²×C₈×C₁₃×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.