Finite Group Databasebeta

#553×C283 #31826150

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

Aliases

direct product#553×C283

Subgroups

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

238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9056

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#49133105, #49133157, #49133231, …
maximal subgroup of#3297×C283, #3301×C283, #3307×C283, …
maximal normal subgroup of#3297×C283, #3301×C283, #3307×C283, …
maximal quotient of#2345×C283, #2347×C283, #2352×C283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18112, 234);