Finite Group Databasebeta

D42×C197 #27160756

order12608
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C197 · Schur multiplier (H2) = C26

Aliases

direct productD42×C197

Subgroups

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

428 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#38741766, #38741828, #38741891, …
maximal subgroup of#1619×C197, #1629×C197, #1639×C197, …
maximal normal subgroup of#1619×C197, #1629×C197, #1639×C197, …
maximal quotient ofD4×C22⋊C4×C197, D4×C4⋊C4×C197, #2358×C197, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12608, 226);