Finite Group Databasebeta

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#562×C197 #27160773

order12608
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C24×C197 · Schur multiplier (H2) = C24

Aliases

direct product#562×C197

Subgroups

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

220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6304

Conjugacy classes & character table

3743 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#38742005, #38742029, #38742035
maximal subgroup of#1656×C197, #1661×C197, #1662×C197, …
maximal normal subgroup of#1656×C197, #1661×C197, #1662×C197, …
maximal quotient of#2376×C197, #2377×C197, #2378×C197, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12608, 243);