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C₂²×M₃₂×C₇₉ #23761027

order	10112
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₇₉ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂²×M₃₂×C₇₉

Subgroups

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

400 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×M₃₂×Dic₇₉, C₂×#23764999, #34440909, …
maximal subgroup of	C₇₉×#12544, C₇₉×#12545, C₂×C₇₉×#1375, …
maximal normal subgroup of	C₇₉×#12544, C₇₉×#12545, C₂×C₇₉×#1375, …
maximal quotient of	C₂²×#346×C₇₉, C₂×C₄×M₃₂×C₇₉, C₂²×C₂²⋊C₁₆×C₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 2137);