Finite Group Databasebeta

D42×C269 #31770282

order17216
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C269 · Schur multiplier (H2) = C26

Aliases

direct productD42×C269

Subgroups

subgroupG/H
center, socleC22×C269C24
commutator, Frattini, cosocleC22C24×C269
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C269 ◁ G

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4304

Conjugacy classes & character table

6725 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46809939, #46810001, #46810064, …
maximal subgroup of#1619×C269, #1629×C269, #1639×C269, …
maximal normal subgroup of#1619×C269, #1629×C269, #1639×C269, …
maximal quotient ofD4×C22⋊C4×C269, D4×C4⋊C4×C269, #2358×C269, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17216, 226);