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#518×C₂₂₇ #28408682

order	14528
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₂₇ · Schur multiplier (H₂) = C₂⁵

Aliases

#518×C₂₂₇

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₂₇	C₂⁴
commutator	C₂	C₂³×C₄×C₂₂₇
Frattini, cosocle	C₂²	C₂⁴×C₂₂₇
prime radical	C₂²×D₄×C₂₂₇	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₂₇ ◁ G

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3632

Conjugacy classes & character table

7718 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#44399842, #44399845, #44399944, …
maximal subgroup of	#1828×C₂₂₇, #1829×C₂₂₇, #1856×C₂₂₇, …
maximal normal subgroup of	#1828×C₂₂₇, #1829×C₂₂₇, #1856×C₂₂₇, …
maximal quotient of	#2273×C₂₂₇, #2274×C₂₂₇, #2275×C₂₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14528, 199);