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2−1+4×C401 #27165641

order12832
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C401 · Schur multiplier (H2) = C25

Aliases

direct product2−1+4×C401

Subgroups

subgroupG/H
center, socleC2×C401C24
commutator, Frattini, cosocleC2C24×C401
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C401 ◁ G

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6416

Conjugacy classes & character table

6817 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#38786287, #38786297, #38786922, …
maximal subgroup of#454×C401, #456×C401, #577×C401, …
maximal normal subgroup of#454×C401, #456×C401, #577×C401, …
maximal quotient of#519×C401, #520×C401, #536×C401, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12832, 50);