Finite Group Databasebeta

D42×C239 #29504449

order15296
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C239 · Schur multiplier (H2) = C26

Aliases

direct productD42×C239

Subgroups

subgroupG/H
center, socleC22×C239C24
commutator, Frattini, cosocleC22C24×C239
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C239 ◁ G

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3824

Conjugacy classes & character table

5975 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44483602, #44483664, #44483727, …
maximal subgroup of#1619×C239, #1629×C239, #1639×C239, …
maximal normal subgroup of#1619×C239, #1629×C239, #1639×C239, …
maximal quotient ofD4×C22⋊C4×C239, D4×C4⋊C4×C239, #2358×C239, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15296, 226);