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C₂⁵×C₄×D₄ #72279447

order	1024
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁷×C₄ · Schur multiplier (H₂) = C₂²⁸

Aliases

C₂⁵×C₄×D₄

Subgroups

	subgroup	G/H
center, socle	C₂⁶×C₄	C₂²
commutator	C₂	C₂⁷×C₄
Frattini, cosocle	C₂²	C₂⁸
prime radical	C₂⁶×D₄	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁶×C₄ ◁ G
LECS	G ▷ C₂² ▷ C₁

1566741 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 512

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂³×#21452, C₂²×D₄×#525, C₂⁵×D₄², …
maximal normal subgroup of	C₂³×#21452, C₂²×D₄×#525, C₂⁵×D₄², …
maximal quotient of	C₂³×#34290, C₂⁴×D₄×C₂²⋊C₄, C₂⁴×C₄×#120, …
automorphism group of	#12038, C₁₆×SD₁₆, #12049, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.