Finite Group Databasebeta

D42×C227 #28408709

order14528
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C227 · Schur multiplier (H2) = C26

Aliases

direct productD42×C227

Subgroups

subgroupG/H
center, socleC22×C227C24
commutator, Frattini, cosocleC22C24×C227
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C227 ◁ G

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3632

Conjugacy classes & character table

5675 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44398788, #44398850, #44398913, …
maximal subgroup of#1619×C227, #1629×C227, #1639×C227, …
maximal normal subgroup of#1619×C227, #1629×C227, #1639×C227, …
maximal quotient ofD4×C22⋊C4×C227, D4×C4⋊C4×C227, #2358×C227, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14528, 226);