Finite Group Databasebeta

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#540×C283 #31826137

order18112
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C283 · Schur multiplier (H2) = C24

Aliases

direct product#540×C283

Subgroups

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

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9056

Conjugacy classes & character table

6226 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49131454, #49131499, #49131547, …
maximal subgroup of#3119×C283, #3122×C283, #3126×C283, …
maximal normal subgroup of#3119×C283, #3122×C283, #3126×C283, …
maximal quotient of#2314×C283, #2319×C283, #2324×C283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18112, 221);