Finite Group Databasebeta

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#562×C281 #31823157

order17984
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C24×C281 · Schur multiplier (H2) = C24

Aliases

direct product#562×C281

Subgroups

subgroupG/H
center, socleC22×C281C24
commutator, Frattini, cosocleC22C24×C281
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C281 ◁ G

220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8992

Conjugacy classes & character table

5339 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49094596, #49094620, #49094626
maximal subgroup of#1656×C281, #1661×C281, #1662×C281, …
maximal normal subgroup of#1656×C281, #1661×C281, #1662×C281, …
maximal quotient of#2376×C281, #2377×C281, #2378×C281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17984, 243);