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2−1+4×C499 #30630255

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

Aliases

direct product2−1+4×C499

Subgroups

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

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7984

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#44543271, #44543281, #44543906, …
maximal subgroup of#454×C499, #456×C499, #577×C499, …
maximal normal subgroup of#454×C499, #456×C499, #577×C499, …
maximal quotient of#519×C499, #520×C499, #536×C499, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15968, 50);