Finite Group Databasebeta

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#562×C263 #30681632

order16832
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C24×C263 · Schur multiplier (H2) = C24

Aliases

direct product#562×C263

Subgroups

subgroupG/H
center, socleC22×C263C24
commutator, Frattini, cosocleC22C24×C263
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C263 ◁ G

220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8416

Conjugacy classes & character table

4997 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46782040, #46782064, #46782070
maximal subgroup of#1656×C263, #1661×C263, #1662×C263, …
maximal normal subgroup of#1656×C263, #1661×C263, #1662×C263, …
maximal quotient of#2376×C263, #2377×C263, #2378×C263, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16832, 243);