Finite Group Databasebeta

D42×C283 #31826142

order18112
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C283 · Schur multiplier (H2) = C26

Aliases

direct productD42×C283

Subgroups

subgroupG/H
center, socleC22×C283C24
commutator, Frattini, cosocleC22C24×C283
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C283 ◁ G

428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4528

Conjugacy classes & character table

7075 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49120315, #49120377, #49120440, …
maximal subgroup of#1619×C283, #1629×C283, #1639×C283, …
maximal normal subgroup of#1619×C283, #1629×C283, #1639×C283, …
maximal quotient ofD4×C22⋊C4×C283, D4×C4⋊C4×C283, #2358×C283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18112, 226);