Finite Group Databasebeta

#392×C257 #30656261

order16448
nilpotency class2
isoclinismisoclinic class of #392
automorphism?
homologyAbelianization (H1) = C23×C257 · Schur multiplier (H2) = C25

Aliases

direct product#392×C257

Subgroups

subgroupG/H
center, socleC23×C257C23
commutator, Frattini, cosocleC23C23×C257
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C257 ◁ G

322 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#45662317, #45663237, #45663242, …
maximal subgroup of#1343×C257, #1595×C257, #1596×C257, …
maximal normal subgroup of#1343×C257, #1595×C257, #1596×C257, …
maximal quotient of#1438×C257, #1439×C257, #1444×C257, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 73);