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#553×C271 #31773582

order17344
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C271 · Schur multiplier (H2) = C24

Aliases

direct product#553×C271

Subgroups

subgroupG/H
center, socleC22×C271C24
commutator, Frattini, cosocleC22C24×C271
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C271 ◁ G

238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8672

Conjugacy classes & character table

6775 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46848208, #46848260, #46848334, …
maximal subgroup of#3297×C271, #3301×C271, #3307×C271, …
maximal normal subgroup of#3297×C271, #3301×C271, #3307×C271, …
maximal quotient of#2345×C271, #2347×C271, #2352×C271, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17344, 234);