Finite Group Databasebeta

← Prev (#31826142) Next (#31826144) →

#546×C283 #31826143

order18112
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C283 · Schur multiplier (H2) = C25

Aliases

direct product#546×C283

Subgroups

subgroupG/H
center, socleC22×C283C24
commutator, Frattini, cosocleC22C24×C283
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C283 ◁ G

334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4528

Conjugacy classes & character table

7075 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49132742, #49132767, #49132782, …
maximal subgroup of#3264×C283, #3266×C283, #3267×C283, …
maximal normal subgroup of#3264×C283, #3266×C283, #3267×C283, …
maximal quotient ofD4×C22⋊C4×C283, #2339×C283, #2342×C283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18112, 227);