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2−1+4×C419 #27211622

order13408
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C419 · Schur multiplier (H2) = C25

Aliases

direct product2−1+4×C419

Subgroups

subgroupG/H
center, socleC2×C419C24
commutator, Frattini, cosocleC2C24×C419
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C419 ◁ G

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6704

Conjugacy classes & character table

7123 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#41000534, #41000544, #41001169, …
maximal subgroup of#454×C419, #456×C419, #577×C419, …
maximal normal subgroup of#454×C419, #456×C419, #577×C419, …
maximal quotient of#519×C419, #520×C419, #536×C419, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13408, 50);