Finite Group Databasebeta

#552×C283 #31826149

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

Aliases

direct product#552×C283

Subgroups

subgroupG/H
center, socleC22×C283C24
commutator, Frattini, cosocleC22C24×C283
prime radicalC2×D4×C283C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C283 ◁ G

214 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#49133090, #49133142, #49133276, …
maximal subgroup of#3296×C283, #3300×C283, #3310×C283, …
maximal normal subgroup of#3296×C283, #3300×C283, #3310×C283, …
maximal quotient of#2343×C283, #2344×C283, #2346×C283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18112, 233);