Finite Group Databasebeta

#550×C263 #30681620

order16832
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C263 · Schur multiplier (H2) = C25

Aliases

direct product#550×C263

Subgroups

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

312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8416

Conjugacy classes & character table

6575 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46781812, #46781874, #46781940, …
maximal subgroup of#1621×C263, #1631×C263, #1641×C263, …
maximal normal subgroup of#1621×C263, #1631×C263, #1641×C263, …
maximal quotient of#2341×C263, Q8×C4⋊C4×C263, #2354×C263, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16832, 231);