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C₂×C₂²⋊C₄×C₄₅₇ #28410428

order	14624
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₄₅₇ · Schur multiplier (H₂) = C₂⁴

Aliases

C₂×C₂²⋊C₄×C₄₅₇

Subgroups

	subgroup	G/H
center, socle	C₂³×C₄₅₇	C₂²
commutator	C₂	C₂²×C₄×C₄₅₇
Frattini, cosocle	C₂²	C₂³×C₄₅₇
prime radical	C₂⁴×C₄₅₇	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₅₇ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7312

Conjugacy classes & character table

9140 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#44416501, #44416543, #44416544, …
maximal subgroup of	#323×C₄₅₇, #342×C₄₅₇, C₄×C₂²⋊C₄×C₄₅₇, …
maximal normal subgroup of	#323×C₄₅₇, #342×C₄₅₇, C₄×C₂²⋊C₄×C₄₅₇, …
maximal quotient of	C₂×#95×C₄₅₇, C₄×C₂²⋊C₄×C₄₅₇, #379×C₄₅₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14624, 22);