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H(5,𝔽2)×C479 #29506285

order15328
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C479 · Schur multiplier (H2) = C25

Aliases

direct productH(5,𝔽2)×C479

Subgroups

subgroupG/H
center, socleC2×C479C24
commutator, Frattini, cosocleC2C24×C479
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C479 ◁ G

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3832

Conjugacy classes & character table

8143 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44500563, #44500573, #44500582, …
maximal subgroup of#453×C479, #455×C479, B(4,𝔽2)×C479, …
maximal normal subgroup of#453×C479, #455×C479, B(4,𝔽2)×C479, …
maximal quotient of#518×C479, #520×C479, #534×C479, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15328, 49);