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C₂×#376×C₇₉ #23759889

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

Aliases

C₂×#376×C₇₉

Subgroups

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

840 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	#376×Dic₇₉, #34209355, #34209366, …
maximal subgroup of	C₂×C₇₉×#1274, C₇₉×#7855, C₇₉×#7906, …
maximal normal subgroup of	C₂×C₇₉×#1274, C₇₉×#7855, C₇₉×#7906, …
maximal quotient of	C₂×C₄×#95×C₇₉, C₄×#376×C₇₉, C₂×C₇₉×#1434, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 999);