Finite Group Databasebeta

D42×C241 #29507394

order15424
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C241 · Schur multiplier (H2) = C26

Aliases

direct productD42×C241

Subgroups

subgroupG/H
center, socleC22×C241C24
commutator, Frattini, cosocleC22C24×C241
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C241 ◁ G

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3856

Conjugacy classes & character table

6025 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44506499, #44506561, #44506624, …
maximal subgroup of#1619×C241, #1629×C241, #1639×C241, …
maximal normal subgroup of#1619×C241, #1629×C241, #1639×C241, …
maximal quotient ofD4×C22⋊C4×C241, D4×C4⋊C4×C241, #2358×C241, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15424, 226);