Finite Group Databasebeta

← Prev (#23760547) Next (#23760549) →

C₂×C₈×D₄×C₇₉ #23760548

order	10112
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₇₉ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×C₈×D₄×C₇₉

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₇₉	C₂²
commutator	C₂	C₂³×C₈×C₇₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₇₉
socle	C₂³×C₇₉	C₂²×C₄
prime radical	C₂²×D₄×C₇₉	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₇₉ ◁ G

616 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	C₂×C₈×#11929609, C₂×C₈×#11929612, C₂×#23762212, …
maximal subgroup of	C₈×#99×C₇₉, C₇₉×#8160, C₈×#100×C₇₉, …
maximal normal subgroup of	C₈×#99×C₇₉, C₇₉×#8160, C₈×#100×C₇₉, …
maximal quotient of	C₂×C₈×D₈×C₇₉, C₂×C₈×SD₁₆×C₇₉, C₂×C₈×Q₁₆×C₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 1658);