Finite Group Databasebeta

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#546×C251 #30631365

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

Aliases

direct product#546×C251

Subgroups

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

334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4016

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#44561846, #44561871, #44561886, …
maximal subgroup of#3264×C251, #3266×C251, #3267×C251, …
maximal normal subgroup of#3264×C251, #3266×C251, #3267×C251, …
maximal quotient ofD4×C22⋊C4×C251, #2339×C251, #2342×C251, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16064, 227);