Finite Group Databasebeta

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#540×C197 #27160751

order12608
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C197 · Schur multiplier (H2) = C24

Aliases

direct product#540×C197

Subgroups

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

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6304

Conjugacy classes & character table

4334 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#38752905, #38752950, #38752998, …
maximal subgroup of#3119×C197, #3122×C197, #3126×C197, …
maximal normal subgroup of#3119×C197, #3122×C197, #3126×C197, …
maximal quotient of#2314×C197, #2319×C197, #2324×C197, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12608, 221);