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C₂×C₄×M₁₆×C₇₉ #23760493

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

Aliases

C₂×C₄×M₁₆×C₇₉

Subgroups

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

656 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×M₁₆×C₇₉⋊C₈, #34253852, C₂×#23761687, …
maximal subgroup of	C₇₉×#7848, C₇₉×#7850, C₇₉×#7852, …
maximal normal subgroup of	C₇₉×#7848, C₇₉×#7850, C₇₉×#7852, …
maximal quotient of	C₂×C₈×M₁₆×C₇₉, C₂×C₇₉×#1451, C₂×C₇₉×#1453, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 1603);