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C₂⁴×C₄×C₈×C₁₇ #72187552

order	8704
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2705829396480
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

C₂⁴×C₄×C₈×C₁₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁶×C₁₇
socle, prime radical	C₂⁶×C₁₇	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

37508 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8704 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₄×C₁₆×C₁₇, C₂⁴×C₈²×C₁₇, C₂³×C₄²×C₈×C₁₇, …
maximal normal subgroup of	C₂⁴×C₄×C₁₆×C₁₇, C₂⁴×C₈²×C₁₇, C₂³×C₄²×C₈×C₁₇, …
maximal quotient of	C₂⁴×C₄×C₁₆×C₁₇, C₂⁴×C₈²×C₁₇, C₂³×C₄²×C₈×C₁₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.