Finite Group Databasebeta

← Prev (#31773568) Next (#31773570) →

#540×C271 #31773569

order17344
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C271 · Schur multiplier (H2) = C24

Aliases

direct product#540×C271

Subgroups

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

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8672

Conjugacy classes & character table

5962 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46846557, #46846602, #46846650, …
maximal subgroup of#3119×C271, #3122×C271, #3126×C271, …
maximal normal subgroup of#3119×C271, #3122×C271, #3126×C271, …
maximal quotient of#2314×C271, #2319×C271, #2324×C271, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17344, 221);