Finite Group Databasebeta

← Prev (#23759803) Next (#23759805) →

Q₈×C₁₆×C₇₉ #23759804

order	10112
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₇₉ · Schur multiplier (H₂) = C₂²

Aliases

Q₈×C₁₆×C₇₉

Subgroups

	subgroup	G/H
center	C₂×C₁₆×C₇₉	C₂²
commutator	C₂	C₂²×C₁₆×C₇₉
Frattini, cosocle	C₂×C₈	C₂³×C₇₉
socle, prime radical	C₂²×C₇₉	C₂²×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₇₉ ◁ G

134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6320 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Q₈×C₁₆×D₇₉, #34441758, #34441771, …
maximal subgroup of	C₇₉×Q₈⋊C₃₂, C₁₆×SD₁₆×C₇₉, C₇₉×#12050, …
maximal normal subgroup of	C₇₉×Q₈⋊C₃₂, C₁₆×SD₁₆×C₇₉, C₇₉×#12050, …
maximal quotient of	C₁₆×C₄⋊C₄×C₇₉, C₇₉×#13104, C₇₉×#13159, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 914);