Finite Group Databasebeta

← Prev (#72193190) Next (#72193192) →

C₂×C₃×C₄×C₈×C₇₉ #72193191

order	15168
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 319488
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₃×C₄×C₈×C₇₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂³×C₃×C₇₉
socle, prime radical	C₂³×C₃×C₇₉	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15168 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₁₆×C₇₉, C₂×C₃×C₈²×C₇₉, C₃×C₄²×C₈×C₇₉, …
maximal normal subgroup of	C₂×C₃×C₄×C₁₆×C₇₉, C₂×C₃×C₈²×C₇₉, C₃×C₄²×C₈×C₇₉, …
maximal quotient of	C₂×C₃×C₄×C₁₆×C₇₉, C₂×C₃×C₈²×C₇₉, C₃×C₄²×C₈×C₇₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.