Finite Group Databasebeta

D42×C281 #31823140

order17984
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C281 · Schur multiplier (H2) = C26

Aliases

direct productD42×C281

Subgroups

subgroupG/H
center, socleC22×C281C24
commutator, Frattini, cosocleC22C24×C281
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C281 ◁ G

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4496

Conjugacy classes & character table

7025 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49094357, #49094419, #49094482, …
maximal subgroup of#1619×C281, #1629×C281, #1639×C281, …
maximal normal subgroup of#1619×C281, #1629×C281, #1639×C281, …
maximal quotient ofD4×C22⋊C4×C281, D4×C4⋊C4×C281, #2358×C281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17984, 226);