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H(5,𝔽2)×C503 #30632767

order16096
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C503 · Schur multiplier (H2) = C25

Aliases

direct productH(5,𝔽2)×C503

Subgroups

subgroupG/H
center, socleC2×C503C24
commutator, Frattini, cosocleC2C24×C503
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C503 ◁ G

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4024

Conjugacy classes & character table

8551 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44566449, #44566459, #44566468, …
maximal subgroup of#453×C503, #455×C503, B(4,𝔽2)×C503, …
maximal normal subgroup of#453×C503, #455×C503, B(4,𝔽2)×C503, …
maximal quotient of#518×C503, #520×C503, #534×C503, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16096, 49);