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H(5,𝔽2)×C499 #30630254

order15968
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C499 · Schur multiplier (H2) = C25

Aliases

direct productH(5,𝔽2)×C499

Subgroups

subgroupG/H
center, socleC2×C499C24
commutator, Frattini, cosocleC2C24×C499
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C499 ◁ G

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3992

Conjugacy classes & character table

8483 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44543266, #44543276, #44543285, …
maximal subgroup of#453×C499, #455×C499, B(4,𝔽2)×C499, …
maximal normal subgroup of#453×C499, #455×C499, B(4,𝔽2)×C499, …
maximal quotient of#518×C499, #520×C499, #534×C499, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15968, 49);