Finite Group Databasebeta

← Prev (#72189337) Next (#72189339) →

C₂×C₈×C₂₅×C₂₇ #72189338

order	10800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5760
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂×C₈×C₂₅×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₅×C₉	C₂²×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₄×C₅×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₆×C₂₅×C₂₇, C₄×C₈×C₂₅×C₂₇, C₂²×C₈×C₂₅×C₂₇, …
maximal normal subgroup of	C₂×C₁₆×C₂₅×C₂₇, C₄×C₈×C₂₅×C₂₇, C₂²×C₈×C₂₅×C₂₇, …
maximal quotient of	C₂×C₁₆×C₂₅×C₂₇, C₄×C₈×C₂₅×C₂₇, C₂²×C₈×C₂₅×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.