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2−1+4×C397 #27163000

order12704
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C397 · Schur multiplier (H2) = C25

Aliases

direct product2−1+4×C397

Subgroups

subgroupG/H
center, socleC2×C397C24
commutator, Frattini, cosocleC2C24×C397
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C397 ◁ G

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6352

Conjugacy classes & character table

6749 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#38762695, #38762705, #38763330, …
maximal subgroup of#454×C397, #456×C397, #577×C397, …
maximal normal subgroup of#454×C397, #456×C397, #577×C397, …
maximal quotient of#519×C397, #520×C397, #536×C397, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12704, 50);