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C₄×#131×C₇₉ #23760496

order	10112
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₇₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₄×#131×C₇₉

Subgroups

	subgroup	G/H
center	C₄×C₈×C₇₉	C₂²
commutator	C₂	C₂²×C₄²×C₇₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₇₉
socle	C₂²×C₇₉	C₂³×C₄
prime radical	C₂×#41×C₇₉	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₇₉ ◁ G

572 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	#131×C₇₉⋊C₈, #34253860, #34253879, …
maximal subgroup of	C₇₉×#8184, C₇₉×#8185, C₇₉×#8186, …
maximal normal subgroup of	C₇₉×#8184, C₇₉×#8185, C₇₉×#8186, …
maximal quotient of	C₈×#131×C₇₉, C₇₉×#17320, C₇₉×#17328, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 1606);