Finite Group Databasebeta

#550×C281 #31823145

order17984
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C281 · Schur multiplier (H2) = C25

Aliases

direct product#550×C281

Subgroups

subgroupG/H
center, socleC22×C281C24
commutator, Frattini, cosocleC22C24×C281
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C281 ◁ G

312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8992

Conjugacy classes & character table

7025 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49094368, #49094430, #49094496, …
maximal subgroup of#1621×C281, #1631×C281, #1641×C281, …
maximal normal subgroup of#1621×C281, #1631×C281, #1641×C281, …
maximal quotient of#2341×C281, Q8×C4⋊C4×C281, #2354×C281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17984, 231);