Finite Group Databasebeta

#550×C197 #27160761

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

Aliases

direct product#550×C197

Subgroups

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

312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6304

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#38741777, #38741839, #38741905, …
maximal subgroup of#1621×C197, #1631×C197, #1641×C197, …
maximal normal subgroup of#1621×C197, #1631×C197, #1641×C197, …
maximal quotient of#2341×C197, Q8×C4⋊C4×C197, #2354×C197, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12608, 231);