Finite Group Databasebeta

#546×C197 #27160757

order12608
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C197 · Schur multiplier (H2) = C25

Aliases

direct product#546×C197

Subgroups

subgroupG/H
center, socleC22×C197C24
commutator, Frattini, cosocleC22C24×C197
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C197 ◁ G

334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3152

Conjugacy classes & character table

4925 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#38754193, #38754218, #38754233, …
maximal subgroup of#3264×C197, #3266×C197, #3267×C197, …
maximal normal subgroup of#3264×C197, #3266×C197, #3267×C197, …
maximal quotient ofD4×C22⋊C4×C197, #2339×C197, #2342×C197, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12608, 227);