Finite Group Databasebeta

D42×C199 #27163695

order12736
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C199 · Schur multiplier (H2) = C26

Aliases

direct productD42×C199

Subgroups

subgroupG/H
center, socleC22×C199C24
commutator, Frattini, cosocleC22C24×C199
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C199 ◁ G

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3184

Conjugacy classes & character table

4975 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#38767904, #38767966, #38768029, …
maximal subgroup of#1619×C199, #1629×C199, #1639×C199, …
maximal normal subgroup of#1619×C199, #1629×C199, #1639×C199, …
maximal quotient ofD4×C22⋊C4×C199, D4×C4⋊C4×C199, #2358×C199, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12736, 226);