Finite Group Databasebeta

#537×C263 #30681607

order16832
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C263 · Schur multiplier (H2) = C25

Aliases

direct product#537×C263

Subgroups

subgroupG/H
center, socleC22×C263C24
commutator, Frattini, cosocleC22C24×C263
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C263 ◁ G

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8416

Conjugacy classes & character table

5786 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46781682, #46781716, #46781750, …
maximal subgroup of#1598×C263, #1604×C263, #1610×C263, …
maximal normal subgroup of#1598×C263, #1604×C263, #1610×C263, …
maximal quotient of#2311×C263, #2316×C263, #2323×C263, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16832, 218);