Finite Group Databasebeta

#537×C239 #29504441

order15296
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C239 · Schur multiplier (H2) = C25

Aliases

direct product#537×C239

Subgroups

subgroupG/H
center, socleC22×C239C24
commutator, Frattini, cosocleC22C24×C239
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C239 ◁ G

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7648

Conjugacy classes & character table

5258 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44483483, #44483517, #44483551, …
maximal subgroup of#1598×C239, #1604×C239, #1610×C239, …
maximal normal subgroup of#1598×C239, #1604×C239, #1610×C239, …
maximal quotient of#2311×C239, #2316×C239, #2323×C239, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15296, 218);