Finite Group Databasebeta

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#552×C271 #31773581

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

Aliases

direct product#552×C271

Subgroups

subgroupG/H
center, socleC22×C271C24
commutator, Frattini, cosocleC22C24×C271
prime radicalC2×D4×C271C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C271 ◁ G

214 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#46848193, #46848245, #46848379, …
maximal subgroup of#3296×C271, #3300×C271, #3310×C271, …
maximal normal subgroup of#3296×C271, #3300×C271, #3310×C271, …
maximal quotient of#2343×C271, #2344×C271, #2346×C271, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17344, 233);