Finite Group Databasebeta

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#562×C211 #27212840

order13504
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C24×C211 · Schur multiplier (H2) = C24

Aliases

direct product#562×C211

Subgroups

subgroupG/H
center, socleC22×C211C24
commutator, Frattini, cosocleC22C24×C211
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C211 ◁ G

220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6752

Conjugacy classes & character table

4009 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#41012691, #41012715, #41012721
maximal subgroup of#1656×C211, #1661×C211, #1662×C211, …
maximal normal subgroup of#1656×C211, #1661×C211, #1662×C211, …
maximal quotient of#2376×C211, #2377×C211, #2378×C211, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13504, 243);