Finite Group Databasebeta

#550×C251 #30631369

order16064
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C251 · Schur multiplier (H2) = C25

Aliases

direct product#550×C251

Subgroups

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

312 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#44549430, #44549492, #44549558, …
maximal subgroup of#1621×C251, #1631×C251, #1641×C251, …
maximal normal subgroup of#1621×C251, #1631×C251, #1641×C251, …
maximal quotient of#2341×C251, Q8×C4⋊C4×C251, #2354×C251, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16064, 231);