Finite Group Databasebeta

#537×C257 #30656406

order16448
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C257 · Schur multiplier (H2) = C25

Aliases

direct product#537×C257

Subgroups

subgroupG/H
center, socleC22×C257C24
commutator, Frattini, cosocleC22C24×C257
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C257 ◁ G

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8224

Conjugacy classes & character table

5654 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#45663255, #45663289, #45663323, …
maximal subgroup of#1598×C257, #1604×C257, #1610×C257, …
maximal normal subgroup of#1598×C257, #1604×C257, #1610×C257, …
maximal quotient of#2311×C257, #2316×C257, #2323×C257, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 218);