Finite Group Databasebeta

#555×C281 #31823150

order17984
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C281 · Schur multiplier (H2) = C23×C4

Aliases

direct product#555×C281

Subgroups

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

236 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#49094386, #49094448, #49094531, …
maximal subgroup of#1624×C281, #1634×C281, #1646×C281, …
maximal normal subgroup of#1624×C281, #1634×C281, #1646×C281, …
maximal quotient of#2346×C281, #2354×C281, #2363×C281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17984, 236);