Finite Group Databasebeta

#552×C251 #30631371

order16064
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C251 · Schur multiplier (H2) = C24

Aliases

direct product#552×C251

Subgroups

subgroupG/H
center, socleC22×C251C24
commutator, Frattini, cosocleC22C24×C251
prime radicalC2×D4×C251C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C251 ◁ G

214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8032

Conjugacy classes & character table

6275 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44562194, #44562246, #44562380, …
maximal subgroup of#3296×C251, #3300×C251, #3310×C251, …
maximal normal subgroup of#3296×C251, #3300×C251, #3310×C251, …
maximal quotient of#2343×C251, #2344×C251, #2346×C251, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16064, 233);